[petsc-users] Residual at the fieldsplit level

[Barry Smith]

  Try ksp_monitor_true_residual. Let's see if it is an issue of preconditioned vs unpreconditioned residual.



> On Sep 16, 2024, at 1:05 PM, miguel.salazar <miguel.salazar at corintis.com> wrote:
> 
> Hello,
>  
> 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.
> 
> ```
> import firedrake as fd
> from firedrake import inner, grad, dx, sin, pi
>  
> N = 10
> mesh = fd.UnitSquareMesh(N, N)
> V = fd.FunctionSpace(mesh, "CG", 1)
> W = V * V
> u = fd.Function(W)
> v = fd.TestFunction(W)
> a = inner(grad(u[0]), grad(v[0])) * dx + inner(grad(u[1]), grad(v[1])) * dx
> x = fd.SpatialCoordinate(mesh)
> f = fd.Function(V)
> f.interpolate(fd.Constant(1e4) * sin(x[0] * pi) * sin(2 * x[1] * pi))
> L = f * v[0] * dx
> F = a - L
> bcs = [fd.DirichletBC(W.sub(0), fd.Constant(2.0), (1,))]
>  
>  
> def snes_firedrake_residual(F, u, bcs):
>     for bcs_ in bcs:
>         bcs_.apply(u)
>     residual = fd.assemble(F, bcs=bcs, zero_bc_nodes=True)
>     with residual.dat.vec_ro as r:
>         print("Initial residual:", r.norm())
>  
>  
> snes_firedrake_residual(F, u, bcs)
>  
>  
> problem = fd.NonlinearVariationalProblem(F, u, bcs=bcs)
> solver_mumps_assembled = {
>     "ksp_type": "preonly",
>     "ksp_monitor": None,
>     "pc_type": "python",
>     "pc_python_type": "firedrake.AssembledPC",
>     "assembled_pc_type": "lu",
>     "assembled_pc_factor_mat_solver_type": "mumps",
>     "assembled_mat_mumps_icntl_14": 200,
>     "assembled_mat_mumps_icntl_24": 1,
> }
> solver_fieldsplit = {
>     "mat_type": "matfree",
>     "snes_type": "newtonls",
>     "ksp_type": "fgmres",
>     "ksp_rtol": 1e-1,
>     "ksp_monitor": None,
>     "pc_type": "fieldsplit",
>     "pc_fieldsplit_type": "additive",
>     "fieldsplit_0": solver_mumps_assembled,
>     "fieldsplit_1": solver_mumps_assembled,
> }
>  
> solver = fd.NonlinearVariationalSolver(problem, solver_parameters=solver_fieldsplit)
> solver.solve()
> ```
> 
> The PETSc output is as follow
> 
> ```
> Initial residual: 462.13689530272404
>   0 SNES Function norm 4.621368953027e+02
>     Residual norms for firedrake_0_ solve.
>     0 KSP Residual norm 4.621368953027e+02
>       Residual norms for firedrake_0_fieldsplit_0_ solve.
>       0 KSP Residual norm 1.000000000000e+00
>       1 KSP Residual norm 3.501082228626e-15
>       Residual norms for firedrake_0_fieldsplit_1_ solve.
>       0 KSP Residual norm 0.000000000000e+00
>       1 KSP Residual norm 0.000000000000e+00
>     1 KSP Residual norm 1.612167203819e-12
>   1 SNES Function norm 1.599350481360e-12
> ```
>  
> Using the fieldsplit additive preconditioner, the problem converges in a single KSP iteration, as expected. However, I do not understand why the residual of fieldsplit_0 (1e+0) does not coincide with the outer residual (462.13689530272404). It should be the case given that only fieldsplit_0 has a non-zero residual contribution. The fact that it is just 1 is suspicious. Is there something about how the fieldsplit works that I am missing?
> 
> Thanks,
> Miguel
> 
> 
> 
> MIGUEL ANGEL SALAZAR DE TROYA
> Head of Software Engineering
> miguel.salazar at corintis.com <mailto:miguel.salazar at corintis.com>
> Corintis SA
> EPFL Innovation Park Building C
> 1015 Lausanne
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