def blocked_solve(): """Blocked version""" Jmat = create_matrix_block(J) Fvec = create_vector_block(F) snes = PETSc.SNES().create(MPI.COMM_WORLD) snes.setTolerances(rtol=1.0e-15, max_it=10) snes.getKSP().setType("preonly") snes.getKSP().getPC().setType("lu") problem = NonlinearPDE_SNESProblem(F, J, [u, p], bcs) snes.setFunction(problem.F_block, Fvec) snes.setJacobian(problem.J_block, J=Jmat, P=None) u.interpolate(initial_guess_u) p.interpolate(initial_guess_p) x = create_vector_block(F) scatter_local_vectors(x, [u.vector.array_r, p.vector.array_r], [(u.function_space.dofmap.index_map, u.function_space.dofmap.index_map_bs), (p.function_space.dofmap.index_map, p.function_space.dofmap.index_map_bs)]) x.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD) snes.solve(None, x) assert snes.getKSP().getConvergedReason() > 0 assert snes.getConvergedReason() > 0 return x.norm()
def test_assembly_solve_taylor_hood_nl(mesh): """Assemble Stokes problem with Taylor-Hood elements and solve.""" gdim = mesh.geometry.dim P2 = VectorFunctionSpace(mesh, ("Lagrange", 2)) P1 = FunctionSpace(mesh, ("Lagrange", 1)) def boundary0(x): """Define boundary x = 0""" return np.isclose(x[0], 0.0) def boundary1(x): """Define boundary x = 1""" return np.isclose(x[0], 1.0) def initial_guess_u(x): u_init = np.row_stack( (np.sin(x[0]) * np.sin(x[1]), np.cos(x[0]) * np.cos(x[1]))) if gdim == 3: u_init = np.row_stack((u_init, np.cos(x[2]))) return u_init def initial_guess_p(x): return -x[0]**2 - x[1]**3 u_bc_0 = Function(P2) u_bc_0.interpolate( lambda x: np.row_stack(tuple(x[j] + float(j) for j in range(gdim)))) u_bc_1 = Function(P2) u_bc_1.interpolate( lambda x: np.row_stack(tuple(np.sin(x[j]) for j in range(gdim)))) facetdim = mesh.topology.dim - 1 bndry_facets0 = locate_entities_boundary(mesh, facetdim, boundary0) bndry_facets1 = locate_entities_boundary(mesh, facetdim, boundary1) bdofs0 = locate_dofs_topological(P2, facetdim, bndry_facets0) bdofs1 = locate_dofs_topological(P2, facetdim, bndry_facets1) bcs = [dirichletbc(u_bc_0, bdofs0), dirichletbc(u_bc_1, bdofs1)] u, p = Function(P2), Function(P1) du, dp = ufl.TrialFunction(P2), ufl.TrialFunction(P1) v, q = ufl.TestFunction(P2), ufl.TestFunction(P1) F = [ inner(ufl.grad(u), ufl.grad(v)) * dx + inner(p, ufl.div(v)) * dx, inner(ufl.div(u), q) * dx ] J = [[derivative(F[0], u, du), derivative(F[0], p, dp)], [derivative(F[1], u, du), derivative(F[1], p, dp)]] P = [[J[0][0], None], [None, inner(dp, q) * dx]] F, J, P = form(F), form(J), form(P) # -- Blocked and monolithic Jmat0 = create_matrix_block(J) Pmat0 = create_matrix_block(P) Fvec0 = create_vector_block(F) snes = PETSc.SNES().create(MPI.COMM_WORLD) snes.setTolerances(rtol=1.0e-15, max_it=10) snes.getKSP().setType("minres") snes.getKSP().getPC().setType("lu") problem = NonlinearPDE_SNESProblem(F, J, [u, p], bcs, P=P) snes.setFunction(problem.F_block, Fvec0) snes.setJacobian(problem.J_block, J=Jmat0, P=Pmat0) u.interpolate(initial_guess_u) p.interpolate(initial_guess_p) x0 = create_vector_block(F) with u.vector.localForm() as _u, p.vector.localForm() as _p: scatter_local_vectors(x0, [_u.array_r, _p.array_r], [(u.function_space.dofmap.index_map, u.function_space.dofmap.index_map_bs), (p.function_space.dofmap.index_map, p.function_space.dofmap.index_map_bs)]) x0.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD) snes.solve(None, x0) assert snes.getConvergedReason() > 0 # -- Blocked and nested Jmat1 = create_matrix_nest(J) Pmat1 = create_matrix_nest(P) Fvec1 = create_vector_nest(F) snes = PETSc.SNES().create(MPI.COMM_WORLD) snes.setTolerances(rtol=1.0e-15, max_it=10) nested_IS = Jmat1.getNestISs() snes.getKSP().setType("minres") snes.getKSP().setTolerances(rtol=1e-12) snes.getKSP().getPC().setType("fieldsplit") snes.getKSP().getPC().setFieldSplitIS(["u", nested_IS[0][0]], ["p", nested_IS[1][1]]) ksp_u, ksp_p = snes.getKSP().getPC().getFieldSplitSubKSP() ksp_u.setType("preonly") ksp_u.getPC().setType('lu') ksp_p.setType("preonly") ksp_p.getPC().setType('lu') problem = NonlinearPDE_SNESProblem(F, J, [u, p], bcs, P=P) snes.setFunction(problem.F_nest, Fvec1) snes.setJacobian(problem.J_nest, J=Jmat1, P=Pmat1) u.interpolate(initial_guess_u) p.interpolate(initial_guess_p) x1 = create_vector_nest(F) for x1_soln_pair in zip(x1.getNestSubVecs(), (u, p)): x1_sub, soln_sub = x1_soln_pair soln_sub.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD) soln_sub.vector.copy(result=x1_sub) x1_sub.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD) x1.set(0.0) snes.solve(None, x1) assert snes.getConvergedReason() > 0 assert nest_matrix_norm(Jmat1) == pytest.approx(Jmat0.norm(), 1.0e-12) assert Fvec1.norm() == pytest.approx(Fvec0.norm(), 1.0e-12) assert x1.norm() == pytest.approx(x0.norm(), 1.0e-12) # -- Monolithic P2_el = ufl.VectorElement("Lagrange", mesh.ufl_cell(), 2) P1_el = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), 1) TH = P2_el * P1_el W = FunctionSpace(mesh, TH) U = Function(W) dU = ufl.TrialFunction(W) u, p = ufl.split(U) du, dp = ufl.split(dU) v, q = ufl.TestFunctions(W) F = inner(ufl.grad(u), ufl.grad(v)) * dx + inner(p, ufl.div(v)) * dx \ + inner(ufl.div(u), q) * dx J = derivative(F, U, dU) P = inner(ufl.grad(du), ufl.grad(v)) * dx + inner(dp, q) * dx F, J, P = form(F), form(J), form(P) bdofsW0_P2_0 = locate_dofs_topological((W.sub(0), P2), facetdim, bndry_facets0) bdofsW0_P2_1 = locate_dofs_topological((W.sub(0), P2), facetdim, bndry_facets1) bcs = [ dirichletbc(u_bc_0, bdofsW0_P2_0, W.sub(0)), dirichletbc(u_bc_1, bdofsW0_P2_1, W.sub(0)) ] Jmat2 = create_matrix(J) Pmat2 = create_matrix(P) Fvec2 = create_vector(F) snes = PETSc.SNES().create(MPI.COMM_WORLD) snes.setTolerances(rtol=1.0e-15, max_it=10) snes.getKSP().setType("minres") snes.getKSP().getPC().setType("lu") problem = NonlinearPDE_SNESProblem(F, J, U, bcs, P=P) snes.setFunction(problem.F_mono, Fvec2) snes.setJacobian(problem.J_mono, J=Jmat2, P=Pmat2) U.sub(0).interpolate(initial_guess_u) U.sub(1).interpolate(initial_guess_p) x2 = create_vector(F) x2.array = U.vector.array_r snes.solve(None, x2) assert snes.getConvergedReason() > 0 assert Jmat2.norm() == pytest.approx(Jmat0.norm(), 1.0e-12) assert Fvec2.norm() == pytest.approx(Fvec0.norm(), 1.0e-12) assert x2.norm() == pytest.approx(x0.norm(), 1.0e-12)
def test_matrix_assembly_block_nl(): """Test assembly of block matrices and vectors into (a) monolithic blocked structures, PETSc Nest structures, and monolithic structures in the nonlinear setting """ mesh = create_unit_square(MPI.COMM_WORLD, 4, 8) p0, p1 = 1, 2 P0 = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), p0) P1 = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), p1) V0 = FunctionSpace(mesh, P0) V1 = FunctionSpace(mesh, P1) def initial_guess_u(x): return np.sin(x[0]) * np.sin(x[1]) def initial_guess_p(x): return -x[0]**2 - x[1]**3 def bc_value(x): return np.cos(x[0]) * np.cos(x[1]) facetdim = mesh.topology.dim - 1 bndry_facets = locate_entities_boundary( mesh, facetdim, lambda x: np.logical_or(np.isclose(x[0], 0.0), np.isclose(x[0], 1.0))) u_bc = Function(V1) u_bc.interpolate(bc_value) bdofs = locate_dofs_topological(V1, facetdim, bndry_facets) bc = dirichletbc(u_bc, bdofs) # Define variational problem du, dp = ufl.TrialFunction(V0), ufl.TrialFunction(V1) u, p = Function(V0), Function(V1) v, q = ufl.TestFunction(V0), ufl.TestFunction(V1) u.interpolate(initial_guess_u) p.interpolate(initial_guess_p) f = 1.0 g = -3.0 F0 = inner(u, v) * dx + inner(p, v) * dx - inner(f, v) * dx F1 = inner(u, q) * dx + inner(p, q) * dx - inner(g, q) * dx a_block = form([[derivative(F0, u, du), derivative(F0, p, dp)], [derivative(F1, u, du), derivative(F1, p, dp)]]) L_block = form([F0, F1]) # Monolithic blocked x0 = create_vector_block(L_block) scatter_local_vectors(x0, [u.vector.array_r, p.vector.array_r], [(u.function_space.dofmap.index_map, u.function_space.dofmap.index_map_bs), (p.function_space.dofmap.index_map, p.function_space.dofmap.index_map_bs)]) x0.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD) # Ghosts are updated inside assemble_vector_block A0 = assemble_matrix_block(a_block, bcs=[bc]) b0 = assemble_vector_block(L_block, a_block, bcs=[bc], x0=x0, scale=-1.0) A0.assemble() assert A0.getType() != "nest" Anorm0 = A0.norm() bnorm0 = b0.norm() # Nested (MatNest) x1 = create_vector_nest(L_block) for x1_soln_pair in zip(x1.getNestSubVecs(), (u, p)): x1_sub, soln_sub = x1_soln_pair soln_sub.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD) soln_sub.vector.copy(result=x1_sub) x1_sub.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD) A1 = assemble_matrix_nest(a_block, bcs=[bc]) b1 = assemble_vector_nest(L_block) apply_lifting_nest(b1, a_block, bcs=[bc], x0=x1, scale=-1.0) for b_sub in b1.getNestSubVecs(): b_sub.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE) bcs0 = bcs_by_block([L.function_spaces[0] for L in L_block], [bc]) set_bc_nest(b1, bcs0, x1, scale=-1.0) A1.assemble() assert A1.getType() == "nest" assert nest_matrix_norm(A1) == pytest.approx(Anorm0, 1.0e-12) assert b1.norm() == pytest.approx(bnorm0, 1.0e-12) # Monolithic version E = P0 * P1 W = FunctionSpace(mesh, E) dU = ufl.TrialFunction(W) U = Function(W) u0, u1 = ufl.split(U) v0, v1 = ufl.TestFunctions(W) U.sub(0).interpolate(initial_guess_u) U.sub(1).interpolate(initial_guess_p) F = inner(u0, v0) * dx + inner(u1, v0) * dx + inner(u0, v1) * dx + inner(u1, v1) * dx \ - inner(f, v0) * ufl.dx - inner(g, v1) * dx J = derivative(F, U, dU) F, J = form(F), form(J) bdofsW_V1 = locate_dofs_topological((W.sub(1), V1), facetdim, bndry_facets) bc = dirichletbc(u_bc, bdofsW_V1, W.sub(1)) A2 = assemble_matrix(J, bcs=[bc]) A2.assemble() b2 = assemble_vector(F) apply_lifting(b2, [J], bcs=[[bc]], x0=[U.vector], scale=-1.0) b2.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE) set_bc(b2, [bc], x0=U.vector, scale=-1.0) assert A2.getType() != "nest" assert A2.norm() == pytest.approx(Anorm0, 1.0e-12) assert b2.norm() == pytest.approx(bnorm0, 1.0e-12)