__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
import numpy as np
import numpy.linalg as la # noqa
import pyopencl as cl
import pyopencl.tools as cl_tools
from meshmode.mesh import BTAG_ALL, BTAG_NONE # noqa
from pytools.obj_array import flat_obj_array
import grudge.geometry as geo
import grudge.op as op
from grudge.array_context import PyOpenCLArrayContext
from grudge.discretization import make_discretization_collection
from grudge.dof_desc import DISCR_TAG_BASE, DISCR_TAG_QUAD, as_dofdesc
from grudge.shortcuts import make_visualizer, rk4_step
logger = logging.getLogger(__name__)
# {{{ wave equation bits
def wave_flux(actx, dcoll, c, w_tpair):
dd = w_tpair.dd
dd_quad = dd.with_discr_tag(DISCR_TAG_QUAD)
u = w_tpair[0]
v = w_tpair[1:]
normal = geo.normal(actx, dcoll, dd)
flux_weak = flat_obj_array(
np.dot(v.avg, normal),
normal*u.avg,
)
# upwind
flux_weak += flat_obj_array(
0.5*(u.ext-u.int),
0.5*normal*np.dot(normal, v.ext-v.int),
)
# FIXME this flux is only correct for continuous c
dd_allfaces_quad = dd_quad.with_domain_tag("all_faces")
c_quad = op.project(dcoll, "vol", dd_quad, c)
flux_quad = op.project(dcoll, dd, dd_quad, flux_weak)
return op.project(dcoll, dd_quad, dd_allfaces_quad, c_quad*flux_quad)
def wave_operator(actx, dcoll, c, w):
u = w[0]
v = w[1:]
dir_u = op.project(dcoll, "vol", BTAG_ALL, u)
dir_v = op.project(dcoll, "vol", BTAG_ALL, v)
dir_bval = flat_obj_array(dir_u, dir_v)
dir_bc = flat_obj_array(-dir_u, dir_v)
dd_quad = as_dofdesc("vol", DISCR_TAG_QUAD)
c_quad = op.project(dcoll, "vol", dd_quad, c)
w_quad = op.project(dcoll, "vol", dd_quad, w)
u_quad = w_quad[0]
v_quad = w_quad[1:]
dd_allfaces_quad = as_dofdesc("all_faces", DISCR_TAG_QUAD)
return (
op.inverse_mass(
dcoll,
flat_obj_array(
-op.weak_local_div(dcoll, dd_quad, c_quad*v_quad),
-op.weak_local_grad(dcoll, dd_quad, c_quad*u_quad)
# pylint: disable=invalid-unary-operand-type
) + op.face_mass(
dcoll,
dd_allfaces_quad,
wave_flux(
actx,
dcoll, c=c,
w_tpair=op.bdry_trace_pair(dcoll,
BTAG_ALL,
interior=dir_bval,
exterior=dir_bc)
) + sum(
wave_flux(actx, dcoll, c=c, w_tpair=tpair)
for tpair in op.interior_trace_pairs(dcoll, w)
)
)
)
)
# }}}
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, width=0.05, center=None):
if center is None:
center = np.array([0.2, 0.35, 0.1])
center = center[:dcoll.dim]
source_omega = 3
nodes = actx.thaw(dcoll.nodes())
center_dist = flat_obj_array([
nodes[i] - center[i]
for i in range(dcoll.dim)
])
return (
np.cos(source_omega*t)
* actx.np.exp(
-np.dot(center_dist, center_dist)
/ width**2))
def main(ctx_factory, dim=2, order=3, visualize=False):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
allocator = cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue))
actx = PyOpenCLArrayContext(queue, allocator=allocator)
nel_1d = 16
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)
from meshmode.discretization.poly_element import (
QuadratureSimplexGroupFactory,
default_simplex_group_factory,
)
dcoll = make_discretization_collection(
actx, mesh,
discr_tag_to_group_factory={
DISCR_TAG_BASE: default_simplex_group_factory(base_dim=dim, order=order),
DISCR_TAG_QUAD: QuadratureSimplexGroupFactory(3*order),
}
)
# bounded above by 1
c = 0.2 + 0.8*bump(actx, dcoll, center=np.zeros(3), width=0.5)
dt = actx.to_numpy(0.5 * estimate_rk4_timestep(actx, dcoll, c=1))
fields = flat_obj_array(
bump(actx, dcoll, ),
[dcoll.zeros(actx) for i in range(dcoll.dim)]
)
vis = make_visualizer(dcoll)
def rhs(t, w):
return wave_operator(actx, dcoll, c=c, w=w)
logger.info("dt = %g", dt)
t = 0
t_final = 3
istep = 0
while t < t_final:
fields = rk4_step(fields, t, dt, rhs)
l2norm = actx.to_numpy(op.norm(dcoll, fields[0], 2))
if istep % 10 == 0:
linfnorm = actx.to_numpy(op.norm(dcoll, fields[0], np.inf))
nodalmax = actx.to_numpy(op.nodal_max(dcoll, "vol", fields[0]))
nodalmin = actx.to_numpy(op.nodal_min(dcoll, "vol", fields[0]))
logger.info("step: %d t: %.8e L2: %.8e Linf: %.8e "
"sol max: %.8e sol min: %.8e",
istep, t, l2norm, linfnorm, nodalmax, nodalmin)
if visualize:
vis.write_vtk_file(
f"fld-wave-eager-var-velocity-{istep:04d}.vtu",
[
("c", c),
("u", fields[0]),
("v", fields[1:]),
]
)
t += dt
istep += 1
# NOTE: These are here to ensure the solution is bounded for the
# time interval specified
assert l2norm < 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")
args = parser.parse_args()
logging.basicConfig(level=logging.INFO)
main(cl.create_some_context,
dim=args.dim,
order=args.order,
visualize=args.visualize)
# vim: foldmethod=marker