def test_wave_accuracy(actx_factory, problem, order, visualize=False):
"""Checks accuracy of the wave operator for a given problem setup.
"""
actx = actx_factory()
p = problem
sym_u, sym_v, sym_f, sym_rhs = sym_wave(p.dim, p.sym_phi)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for n in [8, 10, 12] if p.dim == 3 else [8, 12, 16]:
mesh = p.mesh_factory(n)
from grudge.eager import EagerDGDiscretization
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
def sym_eval(expr, t):
return sym.EvaluationMapper({"c": p.c, "x": nodes, "t": t})(expr)
t_check = 1.23456789
u = sym_eval(sym_u, t_check)
v = sym_eval(sym_v, t_check)
fields = flat_obj_array(u, v)
rhs = wave_operator(discr, c=p.c, w=fields)
rhs[0] = rhs[0] + sym_eval(sym_f, t_check)
expected_rhs = sym_eval(sym_rhs, t_check)
rel_linf_err = actx.to_numpy(
discr.norm(rhs - expected_rhs, np.inf) /
discr.norm(expected_rhs, np.inf))
eoc_rec.add_data_point(1. / n, rel_linf_err)
if visualize:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, discr.order)
vis.write_vtk_file(
"wave_accuracy_{order}_{n}.vtu".format(order=order, n=n), [
("u", fields[0]),
("v", fields[1:]),
("rhs_u_actual", rhs[0]),
("rhs_v_actual", rhs[1:]),
("rhs_u_expected", expected_rhs[0]),
("rhs_v_expected", expected_rhs[1:]),
])
print("Approximation error:")
print(eoc_rec)
assert (eoc_rec.order_estimate() >= order - 0.5
or eoc_rec.max_error() < 1e-11)
def rhs(t, w):
return wave_operator(discr, c=1, w=w)
def get_rhs(t, w):
result = wave_operator(discr, c=p.c, w=w)
result[0] += sym_eval(sym_f, t)
return result
def rhs(t, w):
return wave_operator(discr, c=wave_speed, w=w)