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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