Ahhh, you were so close. Just had to use the dolfin wrappers for the PETSc objects, apply the BCs to the residual in a homogeneous sense, and allow SNES to pass the preconditioner matrix P also.
Corrected code follows (where I’ve used the excellent vtkplotter for visualisation which you can get with pip3 install vtkplotter --user).
from dolfin import *
parameters["form_compiler"]["cpp_optimize"] = True
ffc_options = {"optimize": True, \
"eliminate_zeros": True, \
"precompute_basis_const": True, \
"precompute_ip_const": True}
# Create mesh and define function space
mesh = UnitCubeMesh(24, 16, 16)
V = VectorFunctionSpace(mesh, "Lagrange", 1)
# Mark boundary subdomians
left = CompiledSubDomain("near(x[0], side) && on_boundary", side = 0.0)
right = CompiledSubDomain("near(x[0], side) && on_boundary", side = 1.0)
# Define Dirichlet boundary (x = 0 or x = 1)
c = Expression(("0.0", "0.0", "0.0"), degree=2)
r = Expression(("scale*0.0",
"scale*(y0 + (x[1] - y0)*cos(theta) - (x[2] - z0)*sin(theta) - x[1])",
"scale*(z0 + (x[1] - y0)*sin(theta) + (x[2] - z0)*cos(theta) - x[2])"),
scale = 0.5, y0 = 0.5, z0 = 0.5, theta = pi/3, degree=2)
bcl = DirichletBC(V, c, left)
bcr = DirichletBC(V, r, right)
bcs = [bcl, bcr]
# Define functions
du = TrialFunction(V) # Incremental displacement
v = TestFunction(V) # Test function
u = Function(V) # Displacement from previous iteration
B = Constant((0.0, -0.5, 0.0)) # Body force per unit volume
T = Constant((0.1, 0.0, 0.0)) # Traction force on the boundary
# Kinematics
d = u.geometric_dimension()
I = Identity(d) # Identity tensor
F = I + grad(u) # Deformation gradient
C = F.T*F # Right Cauchy-Green tensor
# Invariants of deformation tensors
Ic = tr(C)
J = det(F)
# Elasticity parameters
E, nu = 10.0, 0.3
mu, lmbda = Constant(E/(2*(1 + nu))), Constant(E*nu/((1 + nu)*(1 - 2*nu)))
# Stored strain energy density (compressible neo-Hookean model)
psi = (mu/2)*(Ic - 3) - mu*ln(J) + (lmbda/2)*(ln(J))**2
# Total potential energy
Pi = psi*dx - dot(B, u)*dx - dot(T, u)*ds
# Compute first variation of Pi (directional derivative about u in the direction of v)
F = derivative(Pi, u, v)
class SNESProblem():
def __init__(self, F, u, bcs):
V = u.function_space()
du = TrialFunction(V)
self.L = F
self.a = derivative(F, u, du)
self.bcs = bcs
self.u = u
def F(self, snes, x, F):
x = PETScVector(x)
F = PETScVector(F)
assemble(self.L, tensor=F)
for bc in self.bcs:
bc.apply(F, x)
def J(self, snes, x, J, P):
J = PETScMatrix(J)
assemble(self.a, tensor=J)
for bc in self.bcs:
bc.apply(J)
problem = SNESProblem(F, u, bcs)
import petsc4py, sys
petsc4py.init(sys.argv)
from petsc4py import PETSc
b = PETScVector() # same as b = PETSc.Vec()
J_mat = PETScMatrix()
snes = PETSc.SNES().create(MPI.comm_world)
snes.setFunction(problem.F, b.vec())
snes.setJacobian(problem.J, J_mat.mat())
snes.solve(None, problem.u.vector().vec())
from vtkplotter.dolfin import plot
plot(u, mode="displace")
