# Copyright (C) 2020 Jørgen S. Dokken # # This file is part of DOLFINX_MPC # # SPDX-License-Identifier: MIT import resource from argparse import ArgumentDefaultsHelpFormatter, ArgumentParser from time import perf_counter import h5py import numpy as np from dolfinx.common import Timer, TimingType, list_timings from dolfinx.fem import (Constant, Function, VectorFunctionSpace, dirichletbc, form, locate_dofs_topological) from dolfinx.fem.petsc import (apply_lifting, assemble_matrix, assemble_vector, set_bc) from dolfinx.io import XDMFFile from dolfinx.log import LogLevel, log, set_log_level from dolfinx.mesh import (CellType, create_unit_cube, locate_entities_boundary, meshtags, refine) from dolfinx_mpc.utils import rigid_motions_nullspace from mpi4py import MPI from petsc4py import PETSc from ufl import (Identity, SpatialCoordinate, TestFunction, TrialFunction, as_vector, ds, dx, grad, inner, sym, tr) def ref_elasticity(tetra: bool = True, r_lvl: int = 0, out_hdf5: h5py.File = None, xdmf: bool = False, boomeramg: bool = False, kspview: bool = False, degree: int = 1): if tetra: N = 3 if degree == 1 else 2 mesh = create_unit_cube(MPI.COMM_WORLD, N, N, N) else: N = 3 mesh = create_unit_cube(MPI.COMM_WORLD, N, N, N, CellType.hexahedron) for i in range(r_lvl): # set_log_level(LogLevel.INFO) N *= 2 if tetra: mesh = refine(mesh, redistribute=True) else: mesh = create_unit_cube(MPI.COMM_WORLD, N, N, N, CellType.hexahedron) # set_log_level(LogLevel.ERROR) N = degree * N fdim = mesh.topology.dim - 1 V = VectorFunctionSpace(mesh, ("Lagrange", int(degree))) # Generate Dirichlet BC on lower boundary (Fixed) u_bc = Function(V) with u_bc.vector.localForm() as u_local: u_local.set(0.0) def boundaries(x): return np.isclose(x[0], np.finfo(float).eps) facets = locate_entities_boundary(mesh, fdim, boundaries) topological_dofs = locate_dofs_topological(V, fdim, facets) bc = dirichletbc(u_bc, topological_dofs) bcs = [bc] # Create traction meshtag def traction_boundary(x): return np.isclose(x[0], 1) t_facets = locate_entities_boundary(mesh, fdim, traction_boundary) facet_values = np.ones(len(t_facets), dtype=np.int32) arg_sort = np.argsort(t_facets) mt = meshtags(mesh, fdim, t_facets[arg_sort], facet_values[arg_sort]) # Elasticity parameters E = PETSc.ScalarType(1.0e4) nu = 0.1 mu = Constant(mesh, E / (2.0 * (1.0 + nu))) lmbda = Constant(mesh, E * nu / ((1.0 + nu) * (1.0 - 2.0 * nu))) g = Constant(mesh, PETSc.ScalarType((0, 0, -1e2))) x = SpatialCoordinate(mesh) f = Constant(mesh, PETSc.ScalarType(1e4)) * \ as_vector((0, -(x[2] - 0.5)**2, (x[1] - 0.5)**2)) # Stress computation def sigma(v): return (2.0 * mu * sym(grad(v)) + lmbda * tr(sym(grad(v))) * Identity(len(v))) # Define variational problem u = TrialFunction(V) v = TestFunction(V) a = inner(sigma(u), grad(v)) * dx rhs = inner(g, v) * ds(domain=mesh, subdomain_data=mt, subdomain_id=1) + inner(f, v) * dx num_dofs = V.dofmap.index_map.size_global * V.dofmap.index_map_bs if MPI.COMM_WORLD.rank == 0: print("Problem size {0:d} ".format(num_dofs)) # Generate reference matrices and unconstrained solution bilinear_form = form(a) A_org = assemble_matrix(bilinear_form, bcs) A_org.assemble() null_space_org = rigid_motions_nullspace(V) A_org.setNearNullSpace(null_space_org) linear_form = form(rhs) L_org = assemble_vector(linear_form) apply_lifting(L_org, [bilinear_form], [bcs]) L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE) set_bc(L_org, bcs) opts = PETSc.Options() if boomeramg: opts["ksp_type"] = "cg" opts["ksp_rtol"] = 1.0e-5 opts["pc_type"] = "hypre" opts['pc_hypre_type'] = 'boomeramg' opts["pc_hypre_boomeramg_max_iter"] = 1 opts["pc_hypre_boomeramg_cycle_type"] = "v" # opts["pc_hypre_boomeramg_print_statistics"] = 1 else: opts["ksp_rtol"] = 1.0e-8 opts["pc_type"] = "gamg" opts["pc_gamg_type"] = "agg" opts["pc_gamg_coarse_eq_limit"] = 1000 opts["pc_gamg_sym_graph"] = True opts["mg_levels_ksp_type"] = "chebyshev" opts["mg_levels_pc_type"] = "jacobi" opts["mg_levels_esteig_ksp_type"] = "cg" opts["matptap_via"] = "scalable" opts["pc_gamg_square_graph"] = 2 opts["pc_gamg_threshold"] = 0.02 # opts["help"] = None # List all available options # opts["ksp_view"] = None # List progress of solver # Create solver, set operator and options solver = PETSc.KSP().create(MPI.COMM_WORLD) solver.setFromOptions() solver.setOperators(A_org) # Solve linear problem u_ = Function(V) start = perf_counter() with Timer("Ref solve"): solver.solve(L_org, u_.vector) end = perf_counter() u_.x.scatter_forward() if kspview: solver.view() it = solver.getIterationNumber() if out_hdf5 is not None: d_set = out_hdf5.get("its") d_set[r_lvl] = it d_set = out_hdf5.get("num_dofs") d_set[r_lvl] = num_dofs d_set = out_hdf5.get("solve_time") d_set[r_lvl, MPI.COMM_WORLD.rank] = end - start if MPI.COMM_WORLD.rank == 0: print("Refinement level {0:d}, Iterations {1:d}".format(r_lvl, it)) # List memory usage mem = sum(MPI.COMM_WORLD.allgather( resource.getrusage(resource.RUSAGE_SELF).ru_maxrss)) if MPI.COMM_WORLD.rank == 0: print("{1:d}: Max usage after trad. solve {0:d} (kb)" .format(mem, r_lvl)) if xdmf: # Name formatting of functions u_.name = "u_unconstrained" fname = "results/ref_elasticity_{0:d}.xdmf".format(r_lvl) with XDMFFile(MPI.COMM_WORLD, fname, "w") as out_xdmf: out_xdmf.write_mesh(mesh) out_xdmf.write_function(u_, 0.0, "Xdmf/Domain/Grid[@Name='{0:s}'][1]".format(mesh.name)) if __name__ == "__main__": parser = ArgumentParser(formatter_class=ArgumentDefaultsHelpFormatter) parser.add_argument("--nref", default=1, type=np.int8, dest="n_ref", help="Number of spatial refinements") parser.add_argument("--degree", default=1, type=np.int8, dest="degree", help="CG Function space degree") parser.add_argument('--xdmf', action='store_true', dest="xdmf", help="XDMF-output of function (Default false)") parser.add_argument('--timings', action='store_true', dest="timings", help="List timings (Default false)") parser.add_argument('--kspview', action='store_true', dest="kspview", help="View PETSc progress") parser.add_argument("-o", default='elasticity_ref.hdf5', dest="hdf5", help="Name of HDF5 output file") ct_parser = parser.add_mutually_exclusive_group(required=False) ct_parser.add_argument('--tet', dest='tetra', action='store_true', help="Tetrahedron elements") ct_parser.add_argument('--hex', dest='tetra', action='store_false', help="Hexahedron elements") solver_parser = parser.add_mutually_exclusive_group(required=False) solver_parser.add_argument('--boomeramg', dest='boomeramg', default=True, action='store_true', help="Use BoomerAMG preconditioner (Default)") solver_parser.add_argument('--gamg', dest='boomeramg', action='store_false', help="Use PETSc GAMG preconditioner") args = parser.parse_args() N = args.n_ref + 1 # Setup hd5f output file h5f = h5py.File(args.hdf5, 'w', driver='mpio', comm=MPI.COMM_WORLD) h5f.create_dataset("its", (N,), dtype=np.int32) h5f.create_dataset("num_dofs", (N,), dtype=np.int32) sd = h5f.create_dataset("solve_time", (N, MPI.COMM_WORLD.size), dtype=np.float64) solver = "BoomerAMG" if args.boomeramg else "GAMG" ct = "Tet" if args.tetra else "Hex" sd.attrs["solver"] = np.string_(solver) sd.attrs["degree"] = np.string_(str(int(args.degree))) sd.attrs["ct"] = np.string_(ct) # Loop over refinement levels for i in range(N): if MPI.COMM_WORLD.rank == 0: set_log_level(LogLevel.INFO) log(LogLevel.INFO, "Run {0:1d} in progress".format(i)) set_log_level(LogLevel.ERROR) ref_elasticity(tetra=args.tetra, r_lvl=i, out_hdf5=h5f, xdmf=args.xdmf, boomeramg=args.boomeramg, kspview=args.kspview, degree=args.degree) if args.timings and i == N - 1: list_timings(MPI.COMM_WORLD, [TimingType.wall]) h5f.close()