<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div><br></div> "formJacobian" should not be __creating__ the matrices. Here "form" means computing the numerical values in the matrix (or when using a shell matrix it means keeping a copy of X so that your custom matrix-free multiply knows the base location where the matrix free Jacobian-vector products are computed.)<div><br></div><div> You create the shell matrices up in your main program and pass them in with SNESSetJacobian(). </div><div><br></div><div> Try first calling SNESSetJacobian() to provide the matrices (provide a dummy function argument) and then call DMSNESSetJacobianLocal() to provide your "formjacobian" function (that does not create the matrices).</div><div><div><br></div><div> Barry</div><div><br></div><div><br></div><div> Yes, "form" is a bad word that should not have been used in our code.</div><div><br></div><div><br id="lineBreakAtBeginningOfMessage"><div><br><blockquote type="cite"><div>On Jan 8, 2024, at 12:24 PM, Yi Hu <y.hu@mpie.de> 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 Experts,<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 implementing a matrix-free jacobian for my SNES solver in Fortran. (command line option -snes_type newtonls -ksp_type gmres)<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">In the main program, I define my residual and jacobian and matrix-free jacobian like the following,<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">…<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">call DMDASNESSetFunctionLocal(DM_mech, INSERT_VALUES, formResidual, PETSC_NULL_SNES, err_PETSc)<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">call DMSNESSetJacobianLocal(DM_mech, formJacobian, PETSC_NULL_SNES, err_PETSc)<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"><o:p> </o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";">subroutine formJacobian(residual_subdomain,F,Jac_pre,Jac,dummy,err_PETSc)<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> <span class="Apple-converted-space"> </span><o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";">#include <petsc/finclude/petscmat.h><o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> use petscmat<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> implicit None<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> DMDALocalInfo, dimension(DMDA_LOCAL_INFO_SIZE) :: &<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> residual_subdomain !< DMDA info (needs to be named "in" for macros like XRANGE to work)<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> real(pREAL), dimension(3,3,cells(1),cells(2),cells3), intent(in) :: &<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> F !< deformation gradient field<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> Mat :: Jac, Jac_pre<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> PetscObject :: dummy<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> PetscErrorCode :: err_PETSc<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> PetscInt :: N_dof ! global number of DoF, maybe only a placeholder<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"><o:p> </o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> N_dof = 9*product(cells(1:2))*cells3<span class="Apple-converted-space"> </span><o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"><o:p> </o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> print*, 'in my jac'<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> <span class="Apple-converted-space"> </span><o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> call MatCreateShell(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N_dof,N_dof,0,Jac,err_PETSc)<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> CHKERRQ(err_PETSc)<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> call MatShellSetOperation(Jac,MATOP_MULT,GK_op,err_PETSc)<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> CHKERRQ(err_PETSc)<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> <span class="Apple-converted-space"> </span><o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> print*, 'in my jac'<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"><o:p> </o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> ! for jac preconditioner<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> call MatCreateShell(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N_dof,N_dof,0,Jac_pre,err_PETSc)<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> CHKERRQ(err_PETSc)<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> call MatShellSetOperation(Jac_pre,MATOP_MULT,GK_op,err_PETSc)<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> CHKERRQ(err_PETSc)<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"><o:p> </o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"> print*, 'in my jac'<o:p></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";"><o:p> </o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10pt; font-family: "Courier New";">end subroutine formJacobian<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><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="hljs-keyword">subroutine</span><span class="line"> GK_op(Jac,dF,output,err_PETSc)</span><o:p></o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="line"> </span><span class="hljs-keyword">real</span><span class="line">(pREAL), </span><span class="hljs-keyword">dimension</span><span class="line">(</span><span class="hljs-number">3</span><span class="line">,</span><span class="hljs-number">3</span><span class="line">,cells(</span><span class="hljs-number">1</span><span class="line">),cells(</span><span class="hljs-number">2</span><span class="line">),cells3), </span><span class="hljs-keyword">intent</span><span class="line">(</span><span class="hljs-keyword">in</span><span class="line">) :: &</span><o:p></o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="line"> dF </span><o:p></o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="line"> </span><span class="hljs-keyword">real</span><span class="line">(pREAL), </span><span class="hljs-keyword">dimension</span><span class="line">(</span><span class="hljs-number">3</span><span class="line">,</span><span class="hljs-number">3</span><span class="line">,cells(</span><span class="hljs-number">1</span><span class="line">),cells(</span><span class="hljs-number">2</span><span class="line">),cells3), </span><span class="hljs-keyword">intent</span><span class="line">(</span><span class="hljs-keyword">out</span><span class="line">) :: &</span><o:p></o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="line"> output </span><o:p></o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="line"> </span><span class="hljs-keyword">real</span><span class="line">(pREAL), </span><span class="hljs-keyword">dimension</span><span class="line">(</span><span class="hljs-number">3</span><span class="line">,</span><span class="hljs-number">3</span><span class="line">) :: &</span><o:p></o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="line"> deltaF_aim = </span><span class="hljs-number">0.0_pREAL</span><o:p></o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><o:p> </o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="line"> Mat :: Jac</span><o:p></o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="line"> PetscErrorCode :: err_PETSc</span><o:p></o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><o:p> </o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="line"> </span><span class="hljs-keyword">integer</span><span class="line"> :: i, j, k, e</span><o:p></o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><o:p> </o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="line"> <span lang="EN-US">… a lot of calculations …<o:p></o:p></span></span></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="line"><span lang="EN-US"><o:p> </o:p></span></span></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="line"> </span><span class="hljs-builtin">print</span><span class="line">*, </span><span class="hljs-string">'in GK op'</span><o:p></o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="line"> </span><o:p></o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><span class="hljs-keyword">end</span><span class="line"> </span><span class="hljs-keyword">subroutine</span><span class="line"> GK_op</span><o:p></o:p></pre><pre style="margin: 0in 0in 0.0001pt; font-size: 10pt; font-family: "Courier New";"><o:p> </o:p></pre><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-US">The first question is that: it seems I still need to explicitly define the interface of MatCreateShell() and MatShellSetOperation() to properly use them, even though I include them via “use petscmat”. It is a little bit strange to me, since some examples do not perform this step.<span class="Apple-converted-space"> </span><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">Then the main issue is that I can build my own Jacobian from my call back function formJacobian, and confirm my Jacobian is a shell matrix (by MatView). However, my customized operator GK_op is not called when solving the nonlinear system (not print my “in GK op”). When I try to monitor my SNES, it gives me some conventional output not mentioning my matrix-free operations. So I guess my customized MATOP_MULT may be not associated with Jacobian. Or my configuration is somehow wrong. Could you help me solve this issue?<span class="Apple-converted-space"> </span><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,<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 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><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); 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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;">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;">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></div></body></html>