Using BDDC as a preconditioner

[hardik-corintis]

Hi! I am trying to use the recently added BDDC preconditioner in Firedrake for a simple nonlinear elasticity problem. I am not sure if I am setting it up correctly. Here is a minimal example of what I am doing:

from firedrake import *
from ufl import variable, grad, det, tr, Identity, ln
import math

# Create a beam-like mesh: long in x-direction, thin in y and z
L, W, H = 10.0, 1.0, 1.0
nx, ny, nz = 40, 4, 4
mesh = BoxMesh(nx, ny, nz, L, W, H)

# Vector function space
V = VectorFunctionSpace(mesh, "CG", 2)

# Displacement field and test function
u = Function(V, name="Displacement")
v = TestFunction(V)

# Deformation gradient and related tensors
d = mesh.geometric_dimension()
I = Identity(d)
F_def = variable(I + grad(u))
C = F_def.T * F_def

# Material parameters (Neo-Hookean)
mu = Constant(1.0)
lmbda = Constant(10.0)

# Invariants
Ic = tr(C)
J = det(F_def)

# Strain energy density
psi = (mu / 2) * (Ic - 3) - mu * ln(J) + (lmbda / 2) * ln(J)**2

# Gravity
rho = Constant(1.0)  # density
g_vec = Constant((0.0, -0.0005, 0.0)) 

# Total potential energy
Pi = psi * dx - rho * dot(g_vec, u) * dx

# First variation (residual)
F = derivative(Pi, u, v)

# Boundary conditions
# Clamp left face (x = 0)
bc_left = DirichletBC(V, Constant((0.0, 0.0, 0.0)), 1)

# Define problem and solver
problem = NonlinearVariationalProblem(F, u, bcs=[bc_left])

solver_parameters_hypre = {
    "snes_type": "newtonls",
    "snes_monitor": None,
    "ksp_type": "stcg",
    # "ksp_monitor": None,
    "ksp_rtol": 1e-4,
    "pc_type": "hypre",
}

solver_parameters_bddc = {
    "snes_type": "newtonls",
    "snes_monitor": None,
    "ksp_type": "gmres",
    # "ksp_monitor": None,
    "ksp_rtol": 1e-4,
    "pc_type": "python",
    "pc_python_type": "firedrake.BDDCPC",
    "bddc_pc_bddc_neumann": {"pc_type": "ilu", "ksp_type": "gmres"},
    "bddc_pc_bddc_dirichlet": {"pc_type": "ilu", "ksp_type": "gmres"},
    "bddc_pc_bddc_coarse": {
        "pc_type": "lu",
        "pc_factor_mat_solver_type": "mumps",  # Replace with 'petsc' if MUMPS is not available
    },
}

solver = NonlinearVariationalSolver(problem, solver_parameters=solver_parameters_bddc)

# Solve
solver.solve()

# Save results
VTKFile("displacement.pvd").write(u)

However, when I execute the script I get the following error:
[0] PCBDDC preconditioner requires matrix of type MATIS

How should I correctly configure the solver or matrix type to use the BDDC preconditioner in Firedrake?
Any help would be greatly appreciated!

[pbrubeck]

BDDC needs a MatIS preconditioner, as you might have already noticed. Currently we only support such matrix type through FDMPC, see this test.

[hardik-corintis]

Thanks for the answer! Is there a plan to support proper MatIS functionality outside of FDMPC in Firedrake in the near future? It would be really helpful to use BDDC in a general setting.

[pbrubeck]

This is in our plans, it should happen after upgrading to pyop3.

[hardik-corintis]

Thanks!