# Copyright (C) 2020 Jørgen S. Dokken # # This file is part of DOLFINX_MPC # # SPDX-License-Identifier: MIT import resource from argparse import ArgumentDefaultsHelpFormatter, ArgumentParser 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, set_bc) from dolfinx.io import XDMFFile from dolfinx.mesh import (CellType, create_unit_cube, locate_entities_boundary, meshtags) from dolfinx_mpc import (MultiPointConstraint, apply_lifting, assemble_matrix, assemble_vector) from dolfinx_mpc.utils import log_info, 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 bench_elasticity_edge(tetra: bool = True, r_lvl: int = 0, out_hdf5=None, xdmf: bool = False, boomeramg: bool = False, kspview: bool = False, degree: int = 1, info: bool = False): N = 3 for i in range(r_lvl): N *= 2 ct = CellType.tetrahedron if tetra else CellType.hexahedron mesh = create_unit_cube(MPI.COMM_WORLD, N, N, N, ct) # Get number of unknowns on each edge V = VectorFunctionSpace(mesh, ("Lagrange", int(degree))) # Generate Dirichlet BC (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) fdim = mesh.topology.dim - 1 facets = locate_entities_boundary(mesh, fdim, boundaries) topological_dofs = locate_dofs_topological(V, fdim, facets) bc = dirichletbc(u_bc, topological_dofs) bcs = [bc] def PeriodicBoundary(x): return np.logical_and(np.isclose(x[0], 1), np.isclose(x[2], 0)) def periodic_relation(x): out_x = np.zeros(x.shape) out_x[0] = x[0] out_x[1] = x[1] out_x[2] = x[2] + 1 return out_x with Timer("~Elasticity: Initialize MPC"): edim = mesh.topology.dim - 2 edges = locate_entities_boundary(mesh, edim, PeriodicBoundary) arg_sort = np.argsort(edges) periodic_mt = meshtags(mesh, edim, edges[arg_sort], np.full(len(edges), 2, dtype=np.int32)) mpc = MultiPointConstraint(V) mpc.create_periodic_constraint_topological(V, periodic_mt, 2, periodic_relation, bcs, scale=0.5) mpc.finalize() # 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) # 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(1e3)) * as_vector((0, -(x[2] - 0.5)**2, (x[1] - 0.5)**2)) # Stress computation def epsilon(v): return sym(grad(v)) def sigma(v): return (2.0 * mu * epsilon(v) + lmbda * tr(epsilon(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 # Setup MPC system if info: log_info(f"Run {r_lvl}: Assembling matrix and vector") bilinear_form = form(a) linear_form = form(rhs) with Timer("~Elasticity: Assemble LHS and RHS"): A = assemble_matrix(bilinear_form, mpc, bcs=bcs) b = assemble_vector(linear_form, mpc) # Create nullspace for elasticity problem and assign to matrix null_space = rigid_motions_nullspace(mpc.function_space) A.setNearNullSpace(null_space) # Apply boundary conditions apply_lifting(b, [bilinear_form], [bcs], mpc) b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE) set_bc(b, 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 # Setup PETSc solver solver = PETSc.KSP().create(MPI.COMM_WORLD) solver.setFromOptions() if info: log_info(f"Run {r_lvl}: Solving") with Timer("~Elasticity: Solve problem") as timer: solver.setOperators(A) uh = b.copy() uh.set(0) solver.solve(b, uh) uh.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD) mpc.backsubstitution(uh) solver_time = timer.elapsed() if kspview: solver.view() mem = sum(MPI.COMM_WORLD.allgather(resource.getrusage(resource.RUSAGE_SELF).ru_maxrss)) it = solver.getIterationNumber() num_dofs = V.dofmap.index_map.size_global * V.dofmap.index_map_bs 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("num_slaves") d_set[r_lvl, MPI.COMM_WORLD.rank] = mpc.num_local_slaves d_set = out_hdf5.get("solve_time") d_set[r_lvl, MPI.COMM_WORLD.rank] = solver_time[0] if info: log_info(f"Lvl: {r_lvl}, Its: {it}, max Mem: {mem}, dim(V): {num_dofs}") if xdmf: # Write solution to file u_h = Function(mpc.function_space) u_h.vector.setArray(uh.array) u_h.name = "u_mpc" fname = f"results/bench_elasticity_edge_{r_lvl}.xdmf" with XDMFFile(MPI.COMM_WORLD, fname, "w") as outfile: outfile.write_mesh(mesh) outfile.write_function(u_h) 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('--info', action='store_true', dest="info", help="Set loglevel to info (Default false)", default=False) parser.add_argument('--kspview', action='store_true', dest="kspview", help="View PETSc progress") 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 h5f = h5py.File('bench_edge_output.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) h5f.create_dataset("num_slaves", (N, MPI.COMM_WORLD.size), 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) for i in range(N): log_info(f"Run {i} in progress") bench_elasticity_edge(tetra=args.tetra, r_lvl=i, out_hdf5=h5f, xdmf=args.xdmf, boomeramg=args.boomeramg, kspview=args.kspview, degree=args.degree, info=args.info) if args.timings and i == N - 1: list_timings(MPI.COMM_WORLD, [TimingType.wall]) h5f.close()