__copyright__ = """ Copyright (C) 2020 Andreas Kloeckner Copyright (C) 2021 University of Illinois Board of Trustees """ __license__ = """ Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. """ import logging from dataclasses import dataclass import numpy as np import pyopencl as cl import pyopencl.tools as cl_tools from arraycontext import dataclass_array_container, with_container_arithmetic from meshmode.dof_array import DOFArray from meshmode.mesh import BTAG_ALL from pytools.obj_array import flat_obj_array, make_obj_array import grudge.geometry as geo import grudge.op as op from grudge.discretization import make_discretization_collection from grudge.dof_desc import DISCR_TAG_BASE, DISCR_TAG_QUAD, as_dofdesc from grudge.shortcuts import compiled_lsrk45_step, make_visualizer from grudge.trace_pair import TracePair logger = logging.getLogger(__name__) from mpi4py import MPI # {{{ wave equation bits @with_container_arithmetic(bcasts_across_obj_array=True, rel_comparison=True, _cls_has_array_context_attr=True, ) @dataclass_array_container @dataclass(frozen=True) class WaveState: u: DOFArray v: np.ndarray # [object array] # NOTE: disable numpy doing any array math __array_ufunc__ = None def __post_init__(self): assert isinstance(self.v, np.ndarray) and self.v.dtype.char == "O" @property def array_context(self): return self.u.array_context def wave_flux(actx, dcoll, c, w_tpair): u = w_tpair.u v = w_tpair.v dd = w_tpair.dd normal = geo.normal(actx, dcoll, dd) flux_weak = WaveState( u=v.avg @ normal, v=u.avg * normal ) # upwind v_jump = v.diff @ normal flux_weak += WaveState( u=0.5 * u.diff, v=0.5 * v_jump * normal, ) return op.project(dcoll, dd, dd.with_domain_tag("all_faces"), c*flux_weak) class _WaveStateTag: pass def wave_operator(actx, dcoll, c, w, quad_tag=None): dd_base = as_dofdesc("vol") dd_vol = as_dofdesc("vol", quad_tag) dd_faces = as_dofdesc("all_faces", quad_tag) dd_btag = as_dofdesc(BTAG_ALL).with_discr_tag(quad_tag) def interp_to_surf_quad(utpair): local_dd = utpair.dd local_dd_quad = local_dd.with_discr_tag(quad_tag) return TracePair( local_dd_quad, interior=op.project(dcoll, local_dd, local_dd_quad, utpair.int), exterior=op.project(dcoll, local_dd, local_dd_quad, utpair.ext) ) w_quad = op.project(dcoll, dd_base, dd_vol, w) u = w_quad.u v = w_quad.v dir_w = op.project(dcoll, dd_base, dd_btag, w) dir_u = dir_w.u dir_v = dir_w.v dir_bval = WaveState(u=dir_u, v=dir_v) dir_bc = WaveState(u=-dir_u, v=dir_v) return ( op.inverse_mass( dcoll, WaveState( u=-c*op.weak_local_div(dcoll, dd_vol, v), v=-c*op.weak_local_grad(dcoll, dd_vol, u) ) + op.face_mass( dcoll, dd_faces, wave_flux( actx, dcoll, c=c, w_tpair=op.bdry_trace_pair(dcoll, dd_btag, interior=dir_bval, exterior=dir_bc) ) + sum( wave_flux(actx, dcoll, c=c, w_tpair=interp_to_surf_quad(tpair)) for tpair in op.interior_trace_pairs(dcoll, w, comm_tag=_WaveStateTag) ) ) ) ) # }}} def estimate_rk4_timestep(actx, dcoll, c): from grudge.dt_utils import characteristic_lengthscales local_dts = characteristic_lengthscales(actx, dcoll) / c return op.nodal_min(dcoll, "vol", local_dts) def bump(actx, dcoll, t=0): source_center = np.array([0.2, 0.35, 0.1])[:dcoll.dim] source_width = 0.05 source_omega = 3 nodes = actx.thaw(dcoll.nodes()) center_dist = flat_obj_array([ nodes[i] - source_center[i] for i in range(dcoll.dim) ]) return ( np.cos(source_omega*t) * actx.np.exp( -np.dot(center_dist, center_dist) / source_width**2)) def main(ctx_factory, dim=2, order=3, visualize=False, lazy=False, numpy=False, use_quad=False, use_nonaffine_mesh=False, no_diagnostics=False): comm = MPI.COMM_WORLD num_parts = comm.size from grudge.array_context import get_reasonable_array_context_class actx_class = get_reasonable_array_context_class(lazy=lazy, distributed=True, numpy=numpy) if numpy: actx = actx_class(comm) else: cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) allocator = cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)) if lazy: actx = actx_class(comm, queue, allocator=allocator, mpi_base_tag=15000) else: actx = actx_class(comm, queue, allocator=allocator) from meshmode.distributed import get_partition_by_pymetis, membership_list_to_map from meshmode.mesh.processing import partition_mesh nel_1d = 16 if comm.rank == 0: if use_nonaffine_mesh: from meshmode.mesh.generation import generate_warped_rect_mesh # FIXME: *generate_warped_rect_mesh* in meshmode warps a # rectangle domain with hard-coded vertices at (-0.5,)*dim # and (0.5,)*dim. Should extend the function interface to allow # for specifying the end points directly. mesh = generate_warped_rect_mesh(dim=dim, order=order, nelements_side=nel_1d) else: from meshmode.mesh.generation import generate_regular_rect_mesh mesh = generate_regular_rect_mesh( a=(-0.5,)*dim, b=(0.5,)*dim, nelements_per_axis=(nel_1d,)*dim) logger.info("%d elements", mesh.nelements) part_id_to_part = partition_mesh(mesh, membership_list_to_map( get_partition_by_pymetis(mesh, num_parts))) parts = [part_id_to_part[i] for i in range(num_parts)] local_mesh = comm.scatter(parts) del mesh else: local_mesh = comm.scatter(None) from meshmode.discretization.poly_element import ( QuadratureSimplexGroupFactory, default_simplex_group_factory, ) dcoll = make_discretization_collection( actx, local_mesh, discr_tag_to_group_factory={ DISCR_TAG_BASE: default_simplex_group_factory(base_dim=dim, order=order), # High-order quadrature to integrate inner products of polynomials # on warped geometry exactly (metric terms are also polynomial) DISCR_TAG_QUAD: QuadratureSimplexGroupFactory(3*order), }) if use_quad: quad_tag = DISCR_TAG_QUAD else: quad_tag = None fields = WaveState( u=bump(actx, dcoll), v=make_obj_array([dcoll.zeros(actx) for i in range(dcoll.dim)]) ) c = 1 # FIXME: Sketchy, empirically determined fudge factor # 5/4 to account for larger LSRK45 stability region dt = actx.to_numpy(0.45 * estimate_rk4_timestep(actx, dcoll, c)) * 5/4 vis = make_visualizer(dcoll) def rhs(t, w): return wave_operator(actx, dcoll, c=c, w=w, quad_tag=quad_tag) compiled_rhs = actx.compile(rhs) if comm.rank == 0: logger.info("dt = %g", dt) import time start = time.time() t = 0 t_final = 3 istep = 0 while t < t_final: start = time.time() fields = compiled_lsrk45_step(actx, fields, t, dt, compiled_rhs) if istep % 10 == 0: stop = time.time() if no_diagnostics: if comm.rank == 0: logger.info("step: %d t: %.8e wall: %.8es", istep, t, stop - start) else: l2norm = actx.to_numpy(op.norm(dcoll, fields.u, 2)) # NOTE: These are here to ensure the solution is bounded for the # time interval specified assert l2norm < 1 linfnorm = actx.to_numpy(op.norm(dcoll, fields.u, np.inf)) nodalmax = actx.to_numpy(op.nodal_max(dcoll, "vol", fields.u)) nodalmin = actx.to_numpy(op.nodal_min(dcoll, "vol", fields.u)) if comm.rank == 0: logger.info("step: %d t: %.8e L2: %.8e Linf: %.8e " "sol max: %.8e sol min: %.8e wall: %.8e", istep, t, l2norm, linfnorm, nodalmax, nodalmin, stop - start) if visualize: vis.write_parallel_vtk_file( comm, f"fld-wave-eager-mpi-{{rank:03d}}-{istep:04d}.vtu", [ ("u", fields.u), ("v", fields.v), ] ) start = stop t += dt istep += 1 if __name__ == "__main__": import argparse parser = argparse.ArgumentParser() parser.add_argument("--dim", default=2, type=int) parser.add_argument("--order", default=3, type=int) parser.add_argument("--visualize", action="store_true") parser.add_argument("--lazy", action="store_true", help="switch to a lazy computation mode") parser.add_argument("--numpy", action="store_true", help="switch to numpy-based array context") parser.add_argument("--quad", action="store_true") parser.add_argument("--nonaffine", action="store_true") parser.add_argument("--no-diagnostics", action="store_true") args = parser.parse_args() logging.basicConfig(level=logging.INFO) main(cl.create_some_context, dim=args.dim, order=args.order, visualize=args.visualize, lazy=args.lazy, numpy=args.numpy, use_quad=args.quad, use_nonaffine_mesh=args.nonaffine, no_diagnostics=args.no_diagnostics) # vim: foldmethod=marker