def create_pcd_problem(F, bcs, J, J_pc, w, nu, boundary_markers, pcd_variant):
W = w.function_space()
# Artificial BC for PCD preconditioner
if pcd_variant == "BRM1":
bc_pcd = DirichletBC(W.sub(1), 0.0, boundary_markers, 1)
elif pcd_variant == "BRM2":
bc_pcd = DirichletBC(W.sub(1), 0.0, boundary_markers, 2)
# Arguments and coefficients of the form
u, p = TrialFunctions(W)
v, q = TestFunctions(W)
# FIXME: Which split is correct? Both work but one might use
# restrict_as_ufc_function
u_, p_ = split(w)
#u_, p_ = w.split()
# PCD operators
mp = Constant(1.0/nu)*p*q*dx
kp = Constant(1.0/nu)*dot(grad(p), u_)*q*dx
ap = inner(grad(p), grad(q))*dx
if pcd_variant == "BRM2":
n = FacetNormal(W.mesh())
ds = Measure("ds", subdomain_data=boundary_markers)
kp -= Constant(1.0/nu)*dot(u_, n)*p*q*ds(1)
#kp -= Constant(1.0/nu)*dot(u_, n)*p*q*ds(0) # TODO: Is this beneficial?
# Collect forms in PCD assembler
pcd_assembler = PCDAssembler(J, F, bcs, J_pc, ap=ap, kp=kp, mp=mp, bcs_pcd=bc_pcd)
# Create nonlinear problem
problem = PCDNonlinearProblem(pcd_assembler)
return problem
f = Constant((0.0,0.0,0.0))
L = inner(f,v)*dx
# PCD operators
mp = Constant(1.0/nu)*p*q*dx
kp = Constant(1.0/nu)*dot(grad(p), u_)*q*dx
ap = inner(grad(p), grad(q))*dx
if args.pcd_variant == "BRM2":
n = FacetNormal(mesh)
ds = Measure("ds", subdomain_data=boundary_markers)
kp -= Constant(1.0/nu)*dot(u_, n)*p*q*ds(1)
#kp -= Constant(1.0/nu)*dot(u_, n)*p*q*ds(0) # TODO: Is this beneficial?
#SystemAssembler(F, L, [bc0, bc1])
# Collect forms to define nonlinear problem
pcd_assembler = PCDAssembler(F, L, [bc0, bc1], ap=ap, kp=kp, mp=mp, bcs_pcd=bc_pcd)
problem = PCDNonlinearProblem(pcd_assembler)
#problem = PCDLinearProblem(pcd_assembler)
# Set up linear solver (GMRES with right preconditioning using Schur fact)
linear_solver = PCDKrylovSolver(comm=mesh.mpi_comm())
linear_solver.parameters["relative_tolerance"] = 1e-10
PETScOptions.set("ksp_monitor")
PETScOptions.set("ksp_gmres_restart", 150)
# Set up subsolvers
PETScOptions.set("fieldsplit_p_pc_python_type", "fenapack.PCDPC_" + args.pcd_variant)
PETScOptions.set("fieldsplit_u_ksp_type", "richardson")
PETScOptions.set("fieldsplit_u_ksp_max_it", 1)
PETScOptions.set("fieldsplit_u_pc_type", "hypre")
PETScOptions.set("fieldsplit_u_pc_hypre_type", "boomeramg")