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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">These are the new options (with ksp_monitor_true_residual)<br>
<br>
solver_mumps_assembled = {<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "ksp_type": "preonly",<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "ksp_monitor": None,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "ksp_monitor_true_residual": None,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "pc_type": "python",<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "pc_python_type": "firedrake.AssembledPC",<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "assembled_pc_type": "lu",<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "assembled_pc_factor_mat_solver_type": "mumps",<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "assembled_mat_mumps_icntl_14": 200,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "assembled_mat_mumps_icntl_24": 1,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">solver_fieldsplit = {<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "mat_type": "matfree",<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "snes_monitor": None,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "snes_type": "newtonls",<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "ksp_type": "fgmres",<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "ksp_monitor_true_residual": None,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">
</span><span lang="IT-CH" style="font-size:11.0pt;mso-fareast-language:EN-US">"ksp_rtol": 1e-1,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="IT-CH" style="font-size:11.0pt;mso-fareast-language:EN-US"> "ksp_monitor": None,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="IT-CH" style="font-size:11.0pt;mso-fareast-language:EN-US">
</span><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">"pc_type": "fieldsplit",<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "pc_fieldsplit_type": "additive",<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "fieldsplit_0": solver_mumps_assembled,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> "fieldsplit_1": solver_mumps_assembled,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">And this is the output<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">Initial residual: 462.13689530272404<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> 0 SNES Function norm 4.621368953027e+02<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> Residual norms for firedrake_0_ solve.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> 0 KSP Residual norm 4.621368953027e+02<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> Residual norms for firedrake_0_ solve.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> 0 KSP unpreconditioned resid norm 4.621368953027e+02 true resid norm 4.621368953027e+02 ||r(i)||/||b|| 1.000000000000e+00<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> Residual norms for firedrake_0_fieldsplit_0_ solve.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> 0 KSP Residual norm 1.000000000000e+00<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> Residual norms for firedrake_0_fieldsplit_0_ solve.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">
</span><span lang="IT-CH" style="font-size:11.0pt;mso-fareast-language:EN-US">0 KSP none resid norm 1.000000000000e+00 true resid norm 3.501082228626e-15 ||r(i)||/||b|| 3.501082228626e-15<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="IT-CH" style="font-size:11.0pt;mso-fareast-language:EN-US"> 1 KSP Residual norm 3.501082228626e-15<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="IT-CH" style="font-size:11.0pt;mso-fareast-language:EN-US"> 1 KSP none resid norm 3.501082228626e-15 true resid norm 3.501082228626e-15 ||r(i)||/||b|| 3.501082228626e-15<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="IT-CH" style="font-size:11.0pt;mso-fareast-language:EN-US">
</span><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">Residual norms for firedrake_0_fieldsplit_1_ solve.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> 0 KSP Residual norm 0.000000000000e+00<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> Residual norms for firedrake_0_fieldsplit_1_ solve.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> 0 KSP none resid norm 0.000000000000e+00 true resid norm 0.000000000000e+00 ||r(i)||/||b|| inf<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> 1 KSP Residual norm 0.000000000000e+00<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> 1 KSP none resid norm 0.000000000000e+00 true resid norm 0.000000000000e+00 ||r(i)||/||b|| inf<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> 1 KSP Residual norm 1.612167203819e-12<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> 1 KSP unpreconditioned resid norm 1.612167203819e-12 true resid norm 1.589286585800e-12 ||r(i)||/||b|| 3.438995245681e-15<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"> 1 SNES Function norm 1.599350481360e-12<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">The true residual is very low. (</span><span lang="IT-CH" style="font-size:11.0pt;mso-fareast-language:EN-US">3.501082228626e-15)</span><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span style="color:black">From:
</span></b><span style="color:black">Barry Smith <bsmith@petsc.dev><br>
<b>Date: </b>Monday, 16 September 2024 at 19:34<br>
<b>To: </b>miguel.salazar <miguel.salazar@corintis.com><br>
<b>Cc: </b>petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject: </b>Re: [petsc-users] Residual at the fieldsplit level<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"> Try ksp_monitor_true_residual. Let's see if it is an issue of preconditioned vs unpreconditioned residual.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><br>
<br>
<o:p></o:p></p>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
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<p class="MsoNormal">On Sep 16, 2024, at 1:05<span style="font-family:"Arial",sans-serif"> </span>PM, miguel.salazar <miguel.salazar@corintis.com> wrote:<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Hello,</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"> </span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">I have this simple example on Firedrake to illustrate my point. I am solving for a two-component poisson equation (uncoupled). Only the first component has a non-zero residual.<br>
<br>
```<br>
</span><span style="font-size:11.0pt">import firedrake as fd<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">from firedrake import inner, grad, dx, sin, pi<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">N = 10<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">mesh = fd.UnitSquareMesh(N, N)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">V = fd.FunctionSpace(mesh, "CG", 1)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">W = V * V<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">u = fd.Function(W)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">v = fd.TestFunction(W)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">a = inner(grad(u[0]), grad(v[0])) * dx + inner(grad(u[1]), grad(v[1])) * dx<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">x = fd.SpatialCoordinate(mesh)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">f = fd.Function(V)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">f.interpolate(fd.Constant(1e4) * sin(x[0] * pi) * sin(2 * x[1] * pi))<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">L = f * v[0] * dx<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">F = a - L<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">bcs = [fd.DirichletBC(W.sub(0), fd.Constant(2.0), (1,))]<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">def snes_firedrake_residual(F, u, bcs):<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> for bcs_ in bcs:<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> bcs_.apply(u)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> residual = fd.assemble(F, bcs=bcs, zero_bc_nodes=True)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> with residual.dat.vec_ro as r:<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> print("Initial residual:", r.norm())<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">snes_firedrake_residual(F, u, bcs)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">problem = fd.NonlinearVariationalProblem(F, u, bcs=bcs)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">solver_mumps_assembled = {<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "ksp_type": "preonly",<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "ksp_monitor": None,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "pc_type": "python",<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "pc_python_type": "firedrake.AssembledPC",<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "assembled_pc_type": "lu",<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "assembled_pc_factor_mat_solver_type": "mumps",<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "assembled_mat_mumps_icntl_14": 200,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "assembled_mat_mumps_icntl_24": 1,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">}<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">solver_fieldsplit = {<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "mat_type": "matfree",<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "snes_type": "newtonls",<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "ksp_type": "fgmres",<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "ksp_rtol": 1e-1,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "ksp_monitor": None,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "pc_type": "fieldsplit",<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "pc_fieldsplit_type": "additive",<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "fieldsplit_0": solver_mumps_assembled,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> "fieldsplit_1": solver_mumps_assembled,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">}<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">solver = fd.NonlinearVariationalSolver(problem, solver_parameters=solver_fieldsplit)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">solver.solve()<o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">```<br>
<br>
The PETSc output is as follow<br>
<br>
```<br>
Initial residual: 462.13689530272404</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"> 0 SNES Function norm 4.621368953027e+02</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<div>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"> Residual norms for firedrake_0_ solve.</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"> 0 KSP Residual norm 4.621368953027e+02</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<div>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"> Residual norms for firedrake_0_fieldsplit_0_ solve.</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"> <span class="apple-converted-space"> </span></span><span lang="IT-CH" style="font-size:11.0pt">0 KSP Residual norm 1.000000000000e+00</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<div>
<p class="MsoNormal"><span lang="IT-CH" style="font-size:11.0pt"> 1 KSP Residual norm 3.501082228626e-15</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<div>
<p class="MsoNormal"><span lang="IT-CH" style="font-size:11.0pt"> <span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size:11.0pt">Residual norms for firedrake_0_fieldsplit_1_ solve.</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<div>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"> <span class="apple-converted-space"> </span></span><span lang="IT-CH" style="font-size:11.0pt">0 KSP Residual norm 0.000000000000e+00</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="IT-CH" style="font-size:11.0pt"> 1 KSP Residual norm 0.000000000000e+00</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<div>
<p class="MsoNormal"><span lang="IT-CH" style="font-size:11.0pt"> <span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size:11.0pt">1 KSP Residual norm 1.612167203819e-12</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<div>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"> 1 SNES Function norm 1.599350481360e-12<br>
```</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"> </span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<div>
<p class="MsoNormal"><span style="font-size:11.0pt">Using the fieldsplit additive preconditioner, the problem converges in a single KSP iteration, as expected. However, I do not understand<span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size:11.0pt">why
the</span><span class="apple-converted-space"><span style="font-size:11.0pt"> </span></span><span style="font-size:11.0pt">residual of fieldsplit_0 (1e+0) does not coincide with the outer residual (462.13689530272404)</span><span lang="EN-US" style="font-size:11.0pt">.
It should be the case given that only<span class="apple-converted-space"> </span></span><span style="font-size:11.0pt">fieldsplit_0 has</span><span class="apple-converted-space"><span lang="EN-US" style="font-size:11.0pt"> </span></span><span lang="EN-US" style="font-size:11.0pt">a
non-zero residual contribution</span><span style="font-size:11.0pt">. The fact that it is just 1 is suspicious. Is there something about how the fieldsplit works that I am missing?</span><span lang="EN-US" style="font-size:11.0pt"><br>
<br>
Thanks,</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Miguel</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="line-height:14.0pt"><b><span style="font-size:8.0pt;font-family:"Arial",sans-serif;color:#1B1464">MIGUEL ANGEL SALAZAR DE TROYA<br>
</span></b><span style="font-size:8.0pt;font-family:"Arial",sans-serif;color:#8A8A8C">Head of Software Engineering<br>
<a href="mailto:miguel.salazar@corintis.com"><em><span style="font-family:"Arial",sans-serif;color:#8A8A8C">miguel.salazar@corintis.com</span></em></a><br>
Corintis SA<br>
EPFL Innovation Park Building C<br>
1015 Lausanne<br>
<br>
<o:p></o:p></span></p>
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<p class="MsoNormal" style="line-height:14.0pt"><span style="font-family:"Arial",sans-serif"><2024-08-1609_02_11-re_mailmigrationfromgoogletooffice365-sebastien.gobel@corintis.com-co_4456a1bf-dd3e-46b7-85f9-21f278e66a79.png><o:p></o:p></span></p>
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