__copyright__ = "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 numpy as np
import meshmode.mesh.generation as mgen
from pytools.obj_array import make_obj_array
from grudge import op, DiscretizationCollection
from grudge.dof_desc import DOFDesc
import pytest
from grudge.array_context import PytestPyOpenCLArrayContextFactory
from arraycontext import pytest_generate_tests_for_array_contexts
pytest_generate_tests = pytest_generate_tests_for_array_contexts(
[PytestPyOpenCLArrayContextFactory])
from arraycontext.container.traversal import thaw
import logging
logger = logging.getLogger(__name__)
# {{{ gradient
@pytest.mark.parametrize("form", ["strong", "weak"])
@pytest.mark.parametrize("dim", [1, 2, 3])
@pytest.mark.parametrize("order", [2, 3])
@pytest.mark.parametrize(("vectorize", "nested"), [
(False, False),
(True, False),
(True, True)
])
def test_gradient(actx_factory, form, dim, order, vectorize, nested,
visualize=False):
actx = actx_factory()
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for n in [4, 6, 8]:
mesh = mgen.generate_regular_rect_mesh(
a=(-1,)*dim, b=(1,)*dim,
nelements_per_axis=(n,)*dim)
dcoll = DiscretizationCollection(actx, mesh, order=order)
def f(x):
result = dcoll.zeros(actx) + 1
for i in range(dim-1):
result = result * actx.np.sin(np.pi*x[i])
result = result * actx.np.cos(np.pi/2*x[dim-1])
return result
def grad_f(x):
result = make_obj_array([dcoll.zeros(actx) + 1 for _ in range(dim)])
for i in range(dim-1):
for j in range(i):
result[i] = result[i] * actx.np.sin(np.pi*x[j])
result[i] = result[i] * np.pi*actx.np.cos(np.pi*x[i])
for j in range(i+1, dim-1):
result[i] = result[i] * actx.np.sin(np.pi*x[j])
result[i] = result[i] * actx.np.cos(np.pi/2*x[dim-1])
for j in range(dim-1):
result[dim-1] = result[dim-1] * actx.np.sin(np.pi*x[j])
result[dim-1] = result[dim-1] * (-np.pi/2*actx.np.sin(np.pi/2*x[dim-1]))
return result
x = thaw(dcoll.nodes(), actx)
if vectorize:
u = make_obj_array([(i+1)*f(x) for i in range(dim)])
else:
u = f(x)
def get_flux(u_tpair):
dd = u_tpair.dd
dd_allfaces = dd.with_dtag("all_faces")
normal = thaw(dcoll.normal(dd), actx)
u_avg = u_tpair.avg
if vectorize:
if nested:
flux = make_obj_array([u_avg_i * normal for u_avg_i in u_avg])
else:
flux = np.outer(u_avg, normal)
else:
flux = u_avg * normal
return op.project(dcoll, dd, dd_allfaces, flux)
dd_allfaces = DOFDesc("all_faces")
if form == "strong":
grad_u = (
op.local_grad(dcoll, u, nested=nested)
# No flux terms because u doesn't have inter-el jumps
)
elif form == "weak":
grad_u = op.inverse_mass(dcoll,
-op.weak_local_grad(dcoll, u, nested=nested) # pylint: disable=E1130
+ # noqa: W504
op.face_mass(dcoll,
dd_allfaces,
# Note: no boundary flux terms here because u_ext == u_int == 0
sum(get_flux(utpair)
for utpair in op.interior_trace_pairs(dcoll, u))
)
)
else:
raise ValueError("Invalid form argument.")
if vectorize:
expected_grad_u = make_obj_array(
[(i+1)*grad_f(x) for i in range(dim)])
if not nested:
expected_grad_u = np.stack(expected_grad_u, axis=0)
else:
expected_grad_u = grad_f(x)
if visualize:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(dcoll, vis_order=order if dim == 3 else dim+3)
filename = (f"test_gradient_{form}_{dim}_{order}"
f"{'_vec' if vectorize else ''}{'_nested' if nested else ''}.vtu")
vis.write_vtk_file(filename, [
("u", u),
("grad_u", grad_u),
("expected_grad_u", expected_grad_u),
], overwrite=True)
rel_linf_err = actx.to_numpy(
op.norm(dcoll, grad_u - expected_grad_u, np.inf)
/ op.norm(dcoll, expected_grad_u, np.inf))
eoc_rec.add_data_point(1./n, rel_linf_err)
print("L^inf error:")
print(eoc_rec)
assert(eoc_rec.order_estimate() >= order - 0.5
or eoc_rec.max_error() < 1e-11)
# }}}
# {{{ divergence
@pytest.mark.parametrize("form", ["strong", "weak"])
@pytest.mark.parametrize("dim", [1, 2, 3])
@pytest.mark.parametrize("order", [2, 3])
@pytest.mark.parametrize(("vectorize", "nested"), [
(False, False),
(True, False),
(True, True)
])
def test_divergence(actx_factory, form, dim, order, vectorize, nested,
visualize=False):
actx = actx_factory()
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for n in [4, 6, 8]:
mesh = mgen.generate_regular_rect_mesh(
a=(-1,)*dim, b=(1,)*dim,
nelements_per_axis=(n,)*dim)
dcoll = DiscretizationCollection(actx, mesh, order=order)
def f(x):
result = make_obj_array([dcoll.zeros(actx) + (i+1) for i in range(dim)])
for i in range(dim-1):
result = result * actx.np.sin(np.pi*x[i])
result = result * actx.np.cos(np.pi/2*x[dim-1])
return result
def div_f(x):
result = dcoll.zeros(actx)
for i in range(dim-1):
deriv = dcoll.zeros(actx) + (i+1)
for j in range(i):
deriv = deriv * actx.np.sin(np.pi*x[j])
deriv = deriv * np.pi*actx.np.cos(np.pi*x[i])
for j in range(i+1, dim-1):
deriv = deriv * actx.np.sin(np.pi*x[j])
deriv = deriv * actx.np.cos(np.pi/2*x[dim-1])
result = result + deriv
deriv = dcoll.zeros(actx) + dim
for j in range(dim-1):
deriv = deriv * actx.np.sin(np.pi*x[j])
deriv = deriv * (-np.pi/2*actx.np.sin(np.pi/2*x[dim-1]))
result = result + deriv
return result
x = thaw(dcoll.nodes(), actx)
if vectorize:
u = make_obj_array([(i+1)*f(x) for i in range(dim)])
if not nested:
u = np.stack(u, axis=0)
else:
u = f(x)
def get_flux(u_tpair):
dd = u_tpair.dd
dd_allfaces = dd.with_dtag("all_faces")
normal = thaw(dcoll.normal(dd), actx)
flux = u_tpair.avg @ normal
return op.project(dcoll, dd, dd_allfaces, flux)
dd_allfaces = DOFDesc("all_faces")
if form == "strong":
div_u = (
op.local_div(dcoll, u)
# No flux terms because u doesn't have inter-el jumps
)
elif form == "weak":
div_u = op.inverse_mass(dcoll,
-op.weak_local_div(dcoll, u)
+ # noqa: W504
op.face_mass(dcoll,
dd_allfaces,
# Note: no boundary flux terms here because u_ext == u_int == 0
sum(get_flux(utpair)
for utpair in op.interior_trace_pairs(dcoll, u))
)
)
else:
raise ValueError("Invalid form argument.")
if vectorize:
expected_div_u = make_obj_array([(i+1)*div_f(x) for i in range(dim)])
else:
expected_div_u = div_f(x)
if visualize:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(dcoll, vis_order=order if dim == 3 else dim+3)
filename = (f"test_divergence_{form}_{dim}_{order}"
f"{'_vec' if vectorize else ''}{'_nested' if nested else ''}.vtu")
vis.write_vtk_file(filename, [
("u", u),
("div_u", div_u),
("expected_div_u", expected_div_u),
], overwrite=True)
rel_linf_err = actx.to_numpy(
op.norm(dcoll, div_u - expected_div_u, np.inf)
/ op.norm(dcoll, expected_div_u, np.inf))
eoc_rec.add_data_point(1./n, rel_linf_err)
print("L^inf error:")
print(eoc_rec)
assert(eoc_rec.order_estimate() >= order - 0.5
or eoc_rec.max_error() < 1e-11)
# }}}
# You can test individual routines by typing
# $ python test_grudge.py 'test_routine()'
if __name__ == "__main__":
import sys
if len(sys.argv) > 1:
exec(sys.argv[1])
else:
pytest.main([__file__])
# vim: fdm=marker