[petsc-users] Residual at the fieldsplit level

Tue Sep 17 00:04:01 CDT 2024

These are the new options (with ksp_monitor_true_residual)

solver_mumps_assembled = {
    "ksp_type": "preonly",
    "ksp_monitor": None,
    "ksp_monitor_true_residual": 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_monitor": None,
    "snes_type": "newtonls",
    "ksp_type": "fgmres",
    "ksp_monitor_true_residual": None,
    "ksp_rtol": 1e-1,
    "ksp_monitor": None,
    "pc_type": "fieldsplit",
    "pc_fieldsplit_type": "additive",
    "fieldsplit_0": solver_mumps_assembled,
    "fieldsplit_1": solver_mumps_assembled,
}

And this is the output

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_ solve.
    0 KSP unpreconditioned resid norm 4.621368953027e+02 true resid norm 4.621368953027e+02 ||r(i)||/||b|| 1.000000000000e+00
      Residual norms for firedrake_0_fieldsplit_0_ solve.
      0 KSP Residual norm 1.000000000000e+00
      Residual norms for firedrake_0_fieldsplit_0_ solve.
      0 KSP none resid norm 1.000000000000e+00 true resid norm 3.501082228626e-15 ||r(i)||/||b|| 3.501082228626e-15
      1 KSP Residual norm 3.501082228626e-15
      1 KSP none resid norm 3.501082228626e-15 true resid norm 3.501082228626e-15 ||r(i)||/||b|| 3.501082228626e-15
      Residual norms for firedrake_0_fieldsplit_1_ solve.
      0 KSP Residual norm 0.000000000000e+00
      Residual norms for firedrake_0_fieldsplit_1_ solve.
      0 KSP none resid norm 0.000000000000e+00 true resid norm 0.000000000000e+00 ||r(i)||/||b|| inf
      1 KSP Residual norm 0.000000000000e+00
      1 KSP none resid norm 0.000000000000e+00 true resid norm 0.000000000000e+00 ||r(i)||/||b|| inf
    1 KSP Residual norm 1.612167203819e-12
    1 KSP unpreconditioned resid norm 1.612167203819e-12 true resid norm 1.589286585800e-12 ||r(i)||/||b|| 3.438995245681e-15
  1 SNES Function norm 1.599350481360e-12

The true residual is very low. (3.501082228626e-15)

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
        [cid:2024-08-1609_02_11-re_mailmigrationfromgoogletooffice365-sebastien.gobel at corintis.com-co_4456a1bf-dd3e-46b7-85f9-21f278e66a79.png]
Here at Corintis we care for your privacy. That is why we have taken appropriate measures to ensure that the data you have provided to us is always secure.
From: Barry Smith <bsmith at petsc.dev>
Date: Monday, 16 September 2024 at 19:34
To: miguel.salazar <miguel.salazar at corintis.com>
Cc: petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Residual at the fieldsplit level

  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

<2024-08-1609_02_11-re_mailmigrationfromgoogletooffice365-sebastien.gobel at corintis.com-co_4456a1bf-dd3e-46b7-85f9-21f278e66a79.png>

Here at Corintis we care for your privacy. That is why we have taken appropriate measures to ensure that the data you have provided to us is always secure.

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