<!DOCTYPE html>
<html>
  <head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
  </head>
  <body>
    <p>Dear Barry,</p>
    <p>Thanks for your help. You suggestion works.</p>
    <p>I found out another approach. I can still use Vec as ctx of my
      MatShell, then I just need to initialize my MatShell with my
      solver Vec x. Then I can use an empty FormJacobShell(), coz my
      MatShell ctx is automatically updated with my solver vec (as I
      initialized with it). In MyMult the ctx of MatShell is the current
      solve vec.</p>
    <p>Best regards,</p>
    <p>Yi<br>
    </p>
    <div class="moz-cite-prefix">On 2/6/24 01:39, Barry Smith wrote:<br>
    </div>
    <blockquote type="cite"
      cite="mid:9FBCF919-112D-4710-AF0B-DA37B62FAD5E@petsc.dev">
      <meta http-equiv="content-type" content="text/html; charset=UTF-8">
      <div><br>
      </div>
        You cannot do call MatShellSetContext(jac,X,ierr) in subroutine
      FormJacobianShell(snes,X,jac,B,dummy,ierr) because Fortran
      arguments are always pass by address and the address of the X
      being passed in may not be valid after the routine that called
      FormJacobianShell() has returned. This is why the GetContext works
      inside this function but not later in MyMult. 
      <div><br>
      </div>
      <div>   Instead add a Vec Xbase member to the MatCtx type and
        update that inside FormJacobShell(). Like</div>
      <div><br>
      </div>
      <div>  TYPE(MatCtx),POINTER :: ctxF_pt
        <div>   MatShellGetContext(jac,ctxF_ptr,ierr)</div>
        <div>   ctxF_pt%Xbase = X</div>
        <div><br>
        </div>
        <div>The reason this works is because ctxF_pt%Xbase = X copies
          the value of X (the PETSc vector) to Xbase, not the address of
          X.</div>
        <div><br>
        </div>
        <div>  Barry</div>
        <div><br>
        </div>
        <div><br>
        </div>
        <div><br>
        </div>
        <div><br>
          <blockquote type="cite">
            <div>On Feb 5, 2024, at 4:18 PM, Yi Hu <a class="moz-txt-link-rfc2396E" href="mailto:y.hu@mpie.de"><y.hu@mpie.de></a>
              wrote:</div>
            <br class="Apple-interchange-newline">
            <div>
              <meta http-equiv="Content-Type"
                content="text/html; charset=UTF-8">
              <div>
                <p>Dear Barry,</p>
                <p>the code is attached. <br>
                </p>
                <p>Just to let you know. When I commented out
                  MatShellSetContext() in FormJacobianShell(), then the
                  code seems to work, meaning that the base vector is
                  passed to shell matrix context behind the scene. <br>
                </p>
                <p>Best regards,</p>
                <p>Yi<br>
                </p>
                <div class="moz-cite-prefix">On 2/5/24 19:09, Barry
                  Smith wrote:<br>
                </div>
                <blockquote type="cite"
cite="mid:2D4940CD-C7A4-4A17-A523-2804488303F1@petsc.dev">
                  <meta http-equiv="content-type"
                    content="text/html; charset=UTF-8">
                  <div><br>
                  </div>
                    Send the entire code.
                  <div><br id="lineBreakAtBeginningOfMessage">
                    <div><br>
                      <blockquote type="cite">
                        <div>On Feb 4, 2024, at 4:43 PM, Yi Hu <a
                            class="moz-txt-link-rfc2396E"
                            href="mailto:y.hu@mpie.de"
                            moz-do-not-send="true"><y.hu@mpie.de></a>
                          wrote:</div>
                        <br class="Apple-interchange-newline">
                        <div>
                          <meta http-equiv="Content-Type"
                            content="text/html; charset=UTF-8">
                          <div>
                            <p>Thanks for your response. You are
                              correct. I overlooked this step.</p>
                            <p>Now I am trying to correct my "shell
                              matrix approach" for ex1f.F90 of snes
                              solver (<a class="moz-txt-link-freetext"
href="https://github.com/hyharry/small_petsc_test/blob/master/test_shell_jac/ex1f.F90"
                                moz-do-not-send="true">https://github.com/hyharry/small_petsc_test/blob/master/test_shell_jac/ex1f.F90</a>).
                              I realized that I need to record the base
                              vector X in the context of shell matrix
                              and then use this info to carry MyMult.
                              However, the context cannot be obtained
                              through MatShellGetContext(). Here are the
                              critical parts of my code.</p>
                            <p>       INTERFACE MatCreateShell<br>
                                       SUBROUTINE
                              MatCreateShell(comm,mloc,nloc,m,n,ctx,mat,ierr)<br>
                                         USE solver_context<br>
                                         MPI_Comm :: comm<br>
                                         PetscInt :: mloc,nloc,m,n<br>
                                         Vec :: ctx<br>
                                         Mat :: mat<br>
                                         PetscErrorCode :: ierr<br>
                                       END SUBROUTINE MatCreateShell<br>
                                     END INTERFACE MatCreateShell<br>
                              <br>
                                     INTERFACE MatShellSetContext<br>
                                       SUBROUTINE
                              MatShellSetContext(mat,ctx,ierr)<br>
                                         USE solver_context<br>
                                         Mat :: mat<br>
                                         !TYPE(MatCtx) :: ctx<br>
                                         Vec :: ctx<br>
                                         PetscErrorCode :: ierr<br>
                                       END SUBROUTINE MatShellSetContext<br>
                                     END INTERFACE MatShellSetContext<br>
                              <br>
                                     INTERFACE MatShellGetContext<br>
                                       SUBROUTINE
                              MatShellGetContext(mat,ctx,ierr)<br>
                                         USE solver_context<br>
                                         Mat :: mat<br>
                                         Vec, Pointer :: ctx<br>
                                         PetscErrorCode :: ierr<br>
                                       END SUBROUTINE MatShellGetContext<br>
                                     END INTERFACE MatShellGetContext</p>
                            <p>in my FormShellJacobian() I did</p>
                            <p>subroutine
                              FormJacobianShell(snes,X,jac,B,dummy,ierr)</p>
                            <p>......<br>
                              <br>
                                call MatShellSetContext(jac,X,ierr)</p>
                            <p>......</p>
                            <p>Then in MyMult() I tried to recover this
                              context by <br>
                            </p>
                            <p>call MatShellGetContext(J,x,ierr)</p>
                            <p>call
                              VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr)<br>
                            </p>
                            <p>Then the program failed with <br>
                            </p>
                            <p>[0]PETSC ERROR: ---------------------
                              Error Message
                              --------------------------------------------------------------<br>
                              [0]PETSC ERROR: Null argument, when
                              expecting valid pointer<br>
                              [0]PETSC ERROR: Null Pointer: Parameter #
                              1<br>
                            </p>
                            <p>In MyMult, I actually defined x to be a
                              pointer. So I am confused here. </p>
                            <p>Best regards,</p>
                            <p>Yi <br>
                            </p>
                            <div class="moz-cite-prefix">On 1/31/24
                              03:18, Barry Smith wrote:<br>
                            </div>
                            <blockquote type="cite"
cite="mid:6C071B22-8D59-4DB8-BCF9-6F31300A648B@petsc.dev">
                              <meta http-equiv="content-type"
                                content="text/html; charset=UTF-8">
                              <div><br>
                              </div>
                                 It is not running an extra KSP
                              iteration. This "extra" matmult is normal
                              and occurs in many of the
                              SNESLineSearchApply_* functions, for
                              example, <a
href="https://petsc.org/release/src/snes/linesearch/impls/bt/linesearchbt.c.html#SNESLineSearchApply_BT"
                                moz-do-not-send="true"
                                class="moz-txt-link-freetext">https://petsc.org/release/src/snes/linesearch/impls/bt/linesearchbt.c.html#SNESLineSearchApply_BT</a> It
                              is used to decide if the Newton step
                              results in sufficient decrease of the
                              function value.
                              <div><br>
                              </div>
                              <div>  Barry<br>
                                <div><br>
                                </div>
                                <div><br
                                    id="lineBreakAtBeginningOfMessage">
                                  <div><br>
                                    <blockquote type="cite">
                                      <div>On Jan 30, 2024, at 3:19 PM,
                                        Yi Hu <a
                                          class="moz-txt-link-rfc2396E"
                                          href="mailto:y.hu@mpie.de"
                                          moz-do-not-send="true"><y.hu@mpie.de></a>
                                        wrote:</div>
                                      <br
class="Apple-interchange-newline">
                                      <div>
                                        <meta http-equiv="Content-Type"
content="text/html; charset=UTF-8">
                                        <div>
                                          <p>Hello Barry,</p>
                                          <p>Thanks for your reply. The
                                            monitor options are fine. I
                                            actually meant my
                                            modification of snes
                                            tutorial ex1f.F90 does not
                                            work and has some unexpected
                                            behavior. I basically wanted
                                            to test if I can use a shell
                                            matrix as my jacobian (code
                                            is here <a
class="moz-txt-link-freetext"
href="https://github.com/hyharry/small_petsc_test/blob/master/test_shell_jac/ex1f.F90"
                                              moz-do-not-send="true">https://github.com/hyharry/small_petsc_test/blob/master/test_shell_jac/ex1f.F90</a>).
                                            After compile my modified
                                            version and run with these
                                            monitor options, it gives me
                                            the following,<br>
                                          </p>
                                          <p> ( in rhs )<br>
                                             ( leave rhs )<br>
                                              0 SNES Function norm
                                            6.041522986797e+00 <br>
                                             ++++++++++++ in jac shell
                                            +++++++++++<br>
                                                0 KSP Residual norm
                                            6.041522986797e+00 <br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                                1 KSP Residual norm
                                            5.065392549852e-16 <br>
                                              Linear solve converged due
                                            to CONVERGED_RTOL iterations
                                            1<br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                              1 SNES Function norm
                                            3.512662245652e+00 <br>
                                             ++++++++++++ in jac shell
                                            +++++++++++<br>
                                                0 KSP Residual norm
                                            3.512662245652e+00 <br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                                1 KSP Residual norm
                                            6.230314124713e-16 <br>
                                              Linear solve converged due
                                            to CONVERGED_RTOL iterations
                                            1<br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                              2 SNES Function norm
                                            8.969285922373e-01 <br>
                                             ++++++++++++ in jac shell
                                            +++++++++++<br>
                                                0 KSP Residual norm
                                            8.969285922373e-01 <br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                                1 KSP Residual norm
                                            0.000000000000e+00 <br>
                                              Linear solve converged due
                                            to CONVERGED_ATOL iterations
                                            1<br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                              3 SNES Function norm
                                            4.863816734540e-01 <br>
                                             ++++++++++++ in jac shell
                                            +++++++++++<br>
                                                0 KSP Residual norm
                                            4.863816734540e-01 <br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                                1 KSP Residual norm
                                            0.000000000000e+00 <br>
                                              Linear solve converged due
                                            to CONVERGED_ATOL iterations
                                            1<br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                              4 SNES Function norm
                                            3.512070785520e-01 <br>
                                             ++++++++++++ in jac shell
                                            +++++++++++<br>
                                                0 KSP Residual norm
                                            3.512070785520e-01 <br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                                1 KSP Residual norm
                                            0.000000000000e+00 <br>
                                              Linear solve converged due
                                            to CONVERGED_ATOL iterations
                                            1<br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                              5 SNES Function norm
                                            2.769700293115e-01 <br>
                                             ++++++++++++ in jac shell
                                            +++++++++++<br>
                                                0 KSP Residual norm
                                            2.769700293115e-01 <br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                                1 KSP Residual norm
                                            1.104778916974e-16 <br>
                                              Linear solve converged due
                                            to CONVERGED_RTOL iterations
                                            1<br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                              6 SNES Function norm
                                            2.055345318150e-01 <br>
                                             ++++++++++++ in jac shell
                                            +++++++++++<br>
                                                0 KSP Residual norm
                                            2.055345318150e-01 <br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                                1 KSP Residual norm
                                            0.000000000000e+00 <br>
                                              Linear solve converged due
                                            to CONVERGED_ATOL iterations
                                            1<br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                              7 SNES Function norm
                                            1.267482220786e-01 <br>
                                             ++++++++++++ in jac shell
                                            +++++++++++<br>
                                                0 KSP Residual norm
                                            1.267482220786e-01 <br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                                1 KSP Residual norm
                                            1.498679601680e-17 <br>
                                              Linear solve converged due
                                            to CONVERGED_RTOL iterations
                                            1<br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                              8 SNES Function norm
                                            3.468150619264e-02 <br>
                                             ++++++++++++ in jac shell
                                            +++++++++++<br>
                                                0 KSP Residual norm
                                            3.468150619264e-02 <br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                                1 KSP Residual norm
                                            5.944160522951e-18 <br>
                                              Linear solve converged due
                                            to CONVERGED_RTOL iterations
                                            1<br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             ( in rhs )<br>
                                             ( leave rhs )<br>
                                             === start mymult ===<br>
                                             === done mymult ===<br>
                                            Nonlinear solve did not
                                            converge due to
                                            DIVERGED_LINE_SEARCH
                                            iterations 8<br>
                                            Number of SNES iterations
                                            =     8<br>
                                          </p>
                                          <p>After each "Linear solve
                                            converged due to
                                            CONVERGED_ATOL iterations",
                                            the code starts to do mymult
                                            again. So I thought it did
                                            an extra (unwanted) KSP
                                            iteration. I would like to
                                            ask if this extra iteration
                                            could be disabled, or maybe
                                            I am wrong about it.</p>
                                          <p>Best regards,</p>
                                          <p>Yi<br>
                                          </p>
                                          <div class="moz-cite-prefix">On
                                            1/30/24 18:35, Barry Smith
                                            wrote:<br>
                                          </div>
                                          <blockquote type="cite"
cite="mid:EAE20968-7A66-449E-8A14-6FBAD06CE0C3@petsc.dev">
                                            <meta
                                              http-equiv="content-type"
content="text/html; charset=UTF-8">
                                            <div><br>
                                            </div>
                                              How do I see a difference?
                                            What does "<span
style="font-family: Calibri, sans-serif;">hence ruin my previous
                                              converged KSP result"
                                              mean? A different answer
                                              at the end of the KSP
                                              solve?</span>
                                            <div><br>
                                            </div>
                                            <div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">$ ./joe >
                                                  joe.basic</span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">~/Src/petsc/src/ksp/ksp/tutorials</span><span
style="font-variant-ligatures: no-common-ligatures; color: #c814c9"><b>
(barry/2023-09-15/fix-log-pcmpi=)</b></span><span
style="font-variant-ligatures: no-common-ligatures"> arch-fix-log-pcmpi</span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">$ ./joe -ksp_monitor
                                                  -ksp_converged_reason
                                                  -snes_monitor >
                                                  joe.monitor</span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">~/Src/petsc/src/ksp/ksp/tutorials</span><span
style="font-variant-ligatures: no-common-ligatures; color: #c814c9"><b>
(barry/2023-09-15/fix-log-pcmpi=)</b></span><span
style="font-variant-ligatures: no-common-ligatures"> arch-fix-log-pcmpi</span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">$ diff joe.basic
                                                  joe.monitor </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">0a1,36</span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   0 SNES
                                                  Function norm
                                                  6.041522986797e+00 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     0 KSP
                                                  Residual norm
                                                  6.041522986797e+00 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     1 KSP
                                                  Residual norm
                                                  5.065392549852e-16 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   Linear solve
                                                  converged due to
                                                  CONVERGED_RTOL_NORMAL
                                                  iterations 1</span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   1 SNES
                                                  Function norm
                                                  3.512662245652e+00 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     0 KSP
                                                  Residual norm
                                                  3.512662245652e+00 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     1 KSP
                                                  Residual norm
                                                  6.230314124713e-16 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   Linear solve
                                                  converged due to
                                                  CONVERGED_RTOL_NORMAL
                                                  iterations 1</span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   2 SNES
                                                  Function norm
                                                  8.969285922373e-01 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     0 KSP
                                                  Residual norm
                                                  8.969285922373e-01 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     1 KSP
                                                  Residual norm
                                                  0.000000000000e+00 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   Linear solve
                                                  converged due to
                                                  CONVERGED_RTOL_NORMAL
                                                  iterations 1</span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   3 SNES
                                                  Function norm
                                                  4.863816734540e-01 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     0 KSP
                                                  Residual norm
                                                  4.863816734540e-01 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     1 KSP
                                                  Residual norm
                                                  0.000000000000e+00 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   Linear solve
                                                  converged due to
                                                  CONVERGED_RTOL_NORMAL
                                                  iterations 1</span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   4 SNES
                                                  Function norm
                                                  3.512070785520e-01 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     0 KSP
                                                  Residual norm
                                                  3.512070785520e-01 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     1 KSP
                                                  Residual norm
                                                  0.000000000000e+00 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   Linear solve
                                                  converged due to
                                                  CONVERGED_RTOL_NORMAL
                                                  iterations 1</span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   5 SNES
                                                  Function norm
                                                  2.769700293115e-01 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     0 KSP
                                                  Residual norm
                                                  2.769700293115e-01 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     1 KSP
                                                  Residual norm
                                                  1.104778916974e-16 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   Linear solve
                                                  converged due to
                                                  CONVERGED_RTOL_NORMAL
                                                  iterations 1</span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   6 SNES
                                                  Function norm
                                                  2.055345318150e-01 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     0 KSP
                                                  Residual norm
                                                  2.055345318150e-01 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     1 KSP
                                                  Residual norm
                                                  1.535110861002e-17 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   Linear solve
                                                  converged due to
                                                  CONVERGED_RTOL_NORMAL
                                                  iterations 1</span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   7 SNES
                                                  Function norm
                                                  1.267482220786e-01 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     0 KSP
                                                  Residual norm
                                                  1.267482220786e-01 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     1 KSP
                                                  Residual norm
                                                  1.498679601680e-17 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   Linear solve
                                                  converged due to
                                                  CONVERGED_RTOL_NORMAL
                                                  iterations 1</span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   8 SNES
                                                  Function norm
                                                  3.468150619264e-02 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     0 KSP
                                                  Residual norm
                                                  3.468150619264e-02 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>     1 KSP
                                                  Residual norm
                                                  5.944160522951e-18 </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures">>   Linear solve
                                                  converged due to
                                                  CONVERGED_RTOL_NORMAL
                                                  iterations 1</span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures"><br>
                                                </span></div>
                                              <div
style="margin: 0px; font-style: normal; font-variant-caps: normal; font-stretch: normal; font-size: 16px; line-height: normal; font-family: Menlo; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"><span
style="font-variant-ligatures: no-common-ligatures"><br>
                                                </span></div>
                                              <div><br>
                                                <blockquote type="cite">
                                                  <div>On Jan 30, 2024,
                                                    at 11:19 AM, Yi Hu <a
class="moz-txt-link-rfc2396E" href="mailto:y.hu@mpie.de"
moz-do-not-send="true"><y.hu@mpie.de></a> wrote:</div>
                                                  <br
class="Apple-interchange-newline">
                                                  <div>
                                                    <meta
                                                      charset="UTF-8">
                                                    <div
class="WordSection1"
style="page: WordSection1; caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                      <div
style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span
                                                          lang="EN-US">Dear
                                                          PETSc team,<o:p></o:p></span></div>
                                                      <div
style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span
                                                          lang="EN-US"><o:p> </o:p></span></div>
                                                      <div
style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span
                                                          lang="EN-US">I
                                                          am still
                                                          trying to sort
                                                          out my
                                                          previous
                                                          thread<span
class="Apple-converted-space"> </span><a
href="https://lists.mcs.anl.gov/pipermail/petsc-users/2024-January/050079.html"
style="color: rgb(149, 79, 114); text-decoration: underline;"
moz-do-not-send="true" class="moz-txt-link-freetext">https://lists.mcs.anl.gov/pipermail/petsc-users/2024-January/050079.html</a><span
class="Apple-converted-space"> </span>using a minimal working example.
                                                          However, I
                                                          encountered
                                                          another
                                                          problem.
                                                          Basically I
                                                          combined the
                                                          basic usage of
                                                          SNES solver
                                                          and shell
                                                          matrix and
                                                          tried to make
                                                          it work. The
                                                          jacobian of my
                                                          snes is
                                                          replaced by a
                                                          customized
                                                          MATOP_MULT.
                                                          The minimal
                                                          example code
                                                          can be viewed
                                                          here<span
class="Apple-converted-space"> </span><a
href="https://github.com/hyharry/small_petsc_test/blob/master/test_shell_jac/ex1f.F90"
style="color: rgb(149, 79, 114); text-decoration: underline;"
moz-do-not-send="true" class="moz-txt-link-freetext">https://github.com/hyharry/small_petsc_test/blob/master/test_shell_jac/ex1f.F90</a><o:p></o:p></span></div>
                                                      <div
style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span
                                                          lang="EN-US"><o:p> </o:p></span></div>
                                                      <div
style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span
                                                          lang="EN-US">When
                                                          running with
                                                          -ksp_monitor
                                                          -ksp_converged_reason,
                                                          it shows an
                                                          extra mymult
                                                          step, and
                                                          hence ruin my
                                                          previous
                                                          converged KSP
                                                          result.
                                                          Implement a
                                                          customized
                                                          converged
                                                          call-back also
                                                          does not help.
                                                          I am wondering
                                                          how to skip
                                                          this extra ksp
                                                          iteration.
                                                          Could anyone
                                                          help me on
                                                          this?<o:p></o:p></span></div>
                                                      <div
style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span
                                                          lang="EN-US"><o:p> </o:p></span></div>
                                                      <div
style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span
                                                          lang="EN-US">Thanks
                                                          for your help.<o:p></o:p></span></div>
                                                      <div
style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span
                                                          lang="EN-US"><o:p> </o:p></span></div>
                                                      <div
style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span
                                                          lang="EN-US">Best
                                                          wishes,<o:p></o:p></span></div>
                                                      <div
style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span
                                                          lang="EN-US">Yi<o:p></o:p></span></div>
                                                    </div>
                                                    <br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <hr
style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">-------------------------------------------------</span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">Stay up to date and follow us on LinkedIn, Twitter and YouTube.</span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">Max-Planck-Institut für Eisenforschung GmbH</span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">Max-Planck-Straße 1</span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">D-40237 Düsseldorf</span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;"> </span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">Handelsregister B 2533 </span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">Amtsgericht Düsseldorf</span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;"> </span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">Geschäftsführung</span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">Prof. Dr. Gerhard Dehm</span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">Prof. Dr. Jörg Neugebauer</span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">Prof. Dr. Dierk Raabe</span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">Dr. Kai de Weldige</span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;"> </span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">Ust.-Id.-Nr.: DE 11 93 58 514 </span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">Steuernummer: 105 5891 1000</span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">Please consider that invitations and e-mails of our institute are </span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">only valid if they end with …@mpie.de. </span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">If you are not sure of the validity please contact </span><a
href="mailto:rco@mpie.de"
style="color: rgb(149, 79, 114); text-decoration: underline; font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;"
moz-do-not-send="true" class="moz-txt-link-freetext">rco@mpie.de</a><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">Bitte beachten Sie, dass Einladungen zu Veranstaltungen und E-Mails</span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">aus unserem Haus nur mit der Endung …@mpie.de gültig sind. </span><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">In Zweifelsfällen wenden Sie sich bitte an </span><a
href="mailto:rco@mpie.de"
style="color: rgb(149, 79, 114); text-decoration: underline; font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;"
moz-do-not-send="true" class="moz-txt-link-freetext">rco@mpie.de</a><br
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
                                                    <span
style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">-------------------------------------------------</span></div>
                                                </blockquote>
                                              </div>
                                              <br>
                                            </div>
                                          </blockquote>
                                          <br>
                                          <br>
                                          <hr>
                                          -------------------------------------------------<br>
Stay up to date and follow us on LinkedIn, Twitter and YouTube.<br>
                                          <br>
Max-Planck-Institut für Eisenforschung GmbH<br>
                                          Max-Planck-Straße 1<br>
                                          D-40237 Düsseldorf<br>
                                           <br>
                                          Handelsregister B 2533 <br>
                                          Amtsgericht Düsseldorf<br>
                                           <br>
                                          Geschäftsführung<br>
                                          Prof. Dr. Gerhard Dehm<br>
                                          Prof. Dr. Jörg Neugebauer<br>
                                          Prof. Dr. Dierk Raabe<br>
                                          Dr. Kai de Weldige<br>
                                           <br>
                                          Ust.-Id.-Nr.: DE 11 93 58 514 <br>
                                          Steuernummer: 105 5891 1000<br>
                                          <br>
                                          <br>
Please consider that invitations and e-mails of our institute are <br>
only valid if they end with …@mpie.de. <br>
If you are not sure of the validity please contact <a
class="moz-txt-link-abbreviated moz-txt-link-freetext"
                                            href="mailto:rco@mpie.de"
                                            moz-do-not-send="true">rco@mpie.de</a><br>
                                          <br>
Bitte beachten Sie, dass Einladungen zu Veranstaltungen und E-Mails<br>
aus unserem Haus nur mit der Endung …@mpie.de gültig sind. <br>
In Zweifelsfällen wenden Sie sich bitte an <a
class="moz-txt-link-abbreviated moz-txt-link-freetext"
                                            href="mailto:rco@mpie.de"
                                            moz-do-not-send="true">rco@mpie.de</a><br>
-------------------------------------------------<br>
                                        </div>
                                      </div>
                                    </blockquote>
                                  </div>
                                  <br>
                                </div>
                              </div>
                            </blockquote>
                            <br>
                            <br>
                            <hr>
                            -------------------------------------------------<br>
Stay up to date and follow us on LinkedIn, Twitter and YouTube.<br>
                            <br>
                            Max-Planck-Institut für Eisenforschung GmbH<br>
                            Max-Planck-Straße 1<br>
                            D-40237 Düsseldorf<br>
                             <br>
                            Handelsregister B 2533 <br>
                            Amtsgericht Düsseldorf<br>
                             <br>
                            Geschäftsführung<br>
                            Prof. Dr. Gerhard Dehm<br>
                            Prof. Dr. Jörg Neugebauer<br>
                            Prof. Dr. Dierk Raabe<br>
                            Dr. Kai de Weldige<br>
                             <br>
                            Ust.-Id.-Nr.: DE 11 93 58 514 <br>
                            Steuernummer: 105 5891 1000<br>
                            <br>
                            <br>
Please consider that invitations and e-mails of our institute are <br>
                            only valid if they end with …@mpie.de. <br>
If you are not sure of the validity please contact <a
class="moz-txt-link-abbreviated moz-txt-link-freetext"
                              href="mailto:rco@mpie.de"
                              moz-do-not-send="true">rco@mpie.de</a><br>
                            <br>
Bitte beachten Sie, dass Einladungen zu Veranstaltungen und E-Mails<br>
aus unserem Haus nur mit der Endung …@mpie.de gültig sind. <br>
                            In Zweifelsfällen wenden Sie sich bitte an <a
class="moz-txt-link-abbreviated moz-txt-link-freetext"
                              href="mailto:rco@mpie.de"
                              moz-do-not-send="true">rco@mpie.de</a><br>
-------------------------------------------------<br>
                          </div>
                        </div>
                      </blockquote>
                    </div>
                    <br>
                  </div>
                </blockquote>
                <br>
                <br>
                <hr>
                -------------------------------------------------<br>
Stay up to date and follow us on LinkedIn, Twitter and YouTube.<br>
                <br>
                Max-Planck-Institut für Eisenforschung GmbH<br>
                Max-Planck-Straße 1<br>
                D-40237 Düsseldorf<br>
                 <br>
                Handelsregister B 2533 <br>
                Amtsgericht Düsseldorf<br>
                 <br>
                Geschäftsführung<br>
                Prof. Dr. Gerhard Dehm<br>
                Prof. Dr. Jörg Neugebauer<br>
                Prof. Dr. Dierk Raabe<br>
                Dr. Kai de Weldige<br>
                 <br>
                Ust.-Id.-Nr.: DE 11 93 58 514 <br>
                Steuernummer: 105 5891 1000<br>
                <br>
                <br>
Please consider that invitations and e-mails of our institute are <br>
                only valid if they end with …@mpie.de. <br>
If you are not sure of the validity please contact <a class="moz-txt-link-abbreviated" href="mailto:rco@mpie.de">rco@mpie.de</a><br>
                <br>
Bitte beachten Sie, dass Einladungen zu Veranstaltungen und E-Mails<br>
aus unserem Haus nur mit der Endung …@mpie.de gültig sind. <br>
                In Zweifelsfällen wenden Sie sich bitte an <a class="moz-txt-link-abbreviated" href="mailto:rco@mpie.de">rco@mpie.de</a><br>
                -------------------------------------------------<br>
              </div>
              <span id="cid:50C19B47-4B2F-4765-A96A-7E47B858EFE8"><ex1f.F90></span></div>
          </blockquote>
        </div>
        <br>
      </div>
    </blockquote>
  <BR />
<BR />
<HR />
-------------------------------------------------<BR />
Stay up to date and follow us on LinkedIn, Twitter and YouTube.<BR />
<BR />
Max-Planck-Institut für Eisenforschung GmbH<BR />
Max-Planck-Straße 1<BR />
D-40237 Düsseldorf<BR />
 <BR />
Handelsregister B 2533 <BR />
Amtsgericht Düsseldorf<BR />
 <BR />
Geschäftsführung<BR />
Prof. Dr. Gerhard Dehm<BR />
Prof. Dr. Jörg Neugebauer<BR />
Prof. Dr. Dierk Raabe<BR />
Dr. Kai de Weldige<BR />
 <BR />
Ust.-Id.-Nr.: DE 11 93 58 514 <BR />
Steuernummer: 105 5891 1000<BR />
<BR />
<BR />
Please consider that invitations and e-mails of our institute are <BR />
only valid if they end with …@mpie.de. <BR />
If you are not sure of the validity please contact rco@mpie.de<BR />
<BR />
Bitte beachten Sie, dass Einladungen zu Veranstaltungen und E-Mails<BR />
aus unserem Haus nur mit der Endung …@mpie.de gültig sind. <BR />
In Zweifelsfällen wenden Sie sich bitte an rco@mpie.de<BR />
-------------------------------------------------<BR />
</body>
</html>