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<p>Dear PETSc community!</p>
<p><br>
</p>
<p>Could you possibly help me with SLEPc generalized eigenproblem issue.</p>
<p>I am trying to solve Ax = \lambda Bx where A and B are positive semi-definite matrices, both have only constant vector in nullspace. To be precise, A is the Schur complement of the Stokes matrix and B is the Laplacian matrix (classical SIMPLE preconditioner). </p>
<p>I specified <span>EPS_GHEP problem type and tried the Krylov-Schur and Lanczos methods. However, they resulted in error "<span>The inner product is not well defined: indefinite matrix".</span></span></p>
<p><span><span><br>
</span></span></p>
<p><span><span>I used <span>EPSSetDeflationSpace() to specify the constant nullspace following slepc manual, and the result were correct for problems <span style="font-family: Calibri, Helvetica, sans-serif, Helvetica, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">Ax = \lambda
x and B<span style="font-family: Calibri, Helvetica, sans-serif, Helvetica, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">x = \lambda x separately.</span></span></span></span></span></p>
<p>I also tried <span style="font-family: Calibri, Helvetica, sans-serif, Helvetica, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">EPS_GHIEP problem type, <span>but got
strange results.</span></span></p>
<p><span style="font-family: Calibri, Helvetica, sans-serif, Helvetica, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"><span><br>
</span></span></p>
<p><span style="font-size: 12pt;">P.S full error message:</span><br>
</p>
<p><span><br>
</span></p>
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<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------</span></p>
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<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: The inner product is not well defined: indefinite matrix</span></p>
<p class="p1" style="margin-right: 0px; margin-left: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: Menlo;">
<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: See https://www.mcs.anl.gov/petsc/documentation/faq.html for trouble shooting.</span></p>
<p class="p1" style="margin-right: 0px; margin-left: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: Menlo;">
<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: Petsc Release Version 3.13.4, Aug 01, 2020<span class="Apple-converted-space"> </span></span></p>
<p class="p1" style="margin-right: 0px; margin-left: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: Menlo;">
<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: ./scopes_slepc on a linux-gnu-real-32 named 608add14733f by hydra Thu Dec<span class="Apple-converted-space">
</span>9 23:38:43 2021</span></p>
<p class="p1" style="margin-right: 0px; margin-left: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: Menlo;">
<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: Configure options PETSC_ARCH=linux-gnu-real-32 --COPTFLAGS=-O3 -march=native -mtune=native --CXXOPTFLAGS=-O3 -march=native -mtune=native --FOPTFLAGS=-O3 -march=native -mtune=native
--with-debugging=0 --with-fortran-bindings=0 --with-shared-libraries --download-hdf5 --download-blacs --download-hypre --download-metis --download-parmetis --download-mumps --download-ptscotch --download-scalapack --download-spai --download-suitesparse --with-scalar-type=real</span></p>
<p class="p1" style="margin-right: 0px; margin-left: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: Menlo;">
<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: #1 BV_SafeSqrt() line 128 in /usr/local/slepc/include/slepc/private/bvimpl.h</span></p>
<p class="p1" style="margin-right: 0px; margin-left: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: Menlo;">
<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: #2 BVNorm_Private() line 473 in /usr/local/slepc/src/sys/classes/bv/interface/bvglobal.c</span></p>
<p class="p1" style="margin-right: 0px; margin-left: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: Menlo;">
<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: #3 BVNormVec() line 586 in /usr/local/slepc/src/sys/classes/bv/interface/bvglobal.c</span></p>
<p class="p1" style="margin-right: 0px; margin-left: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: Menlo;">
<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: #4 BVOrthogonalizeMGS1() line 65 in /usr/local/slepc/src/sys/classes/bv/interface/bvorthog.c</span></p>
<p class="p1" style="margin-right: 0px; margin-left: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: Menlo;">
<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: #5 BVOrthogonalizeGS() line 188 in /usr/local/slepc/src/sys/classes/bv/interface/bvorthog.c</span></p>
<p class="p1" style="margin-right: 0px; margin-left: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: Menlo;">
<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: #6 BVOrthogonalizeColumn() line 348 in /usr/local/slepc/src/sys/classes/bv/interface/bvorthog.c</span></p>
<p class="p1" style="margin-right: 0px; margin-left: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: Menlo;">
<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: #7 BVInsertVecs() line 363 in /usr/local/slepc/src/sys/classes/bv/interface/bvfunc.c</span></p>
<p class="p1" style="margin-right: 0px; margin-left: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: Menlo;">
<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: #8 BVInsertConstraints() line 434 in /usr/local/slepc/src/sys/classes/bv/interface/bvfunc.c</span></p>
<p class="p1" style="margin-right: 0px; margin-left: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: Menlo;">
<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: #9 EPSSetUp() line 308 in /usr/local/slepc/src/eps/interface/epssetup.c</span></p>
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<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: #10 EPSSolve() line 136 in /usr/local/slepc/src/eps/interface/epssolve.c</span></p>
<p class="p1" style="margin-right: 0px; margin-left: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: Menlo;">
<span class="s1" style="font-variant-ligatures: no-common-ligatures;">[0]PETSC ERROR: #11 computeCond() line 1634 in scopes_slepc.cpp</span></p>
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<p>Thank you in advance!</p>
<p>Sincerely,</p>
<p>Vladislav Pimanov</p>
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