def flux_num(self, q, fluxes, bdry_tag_state_flux):
n = self.len_q
d = len(fluxes)
fvph = FluxVectorPlaceholder(n*(d+1)+1)
speed_ph = fvph[0]
state_ph = fvph[1:n+1]
fluxes_ph = [fvph[i*n+1:(i+1)*n+1] for i in range(1,d+1)]
normal = make_normal(d)
flux_strong = 0.5*sum(n_i*(f_i.ext-f_i.int) for n_i, f_i in zip(normal, fluxes_ph))
if self.flux_type == "central":
pass
elif self.flux_type == "lf":
penalty = flux_max(speed_ph.int,speed_ph.ext)*(state_ph.ext-state_ph.int)
flux_strong = 0.5 * penalty + flux_strong
else:
raise ValueError("Invalid flux type '%s'" % self.flux_type)
flux_op = get_flux_operator(flux_strong)
int_operand = join_fields(self.wave_speed(q), q, *fluxes)
return (flux_op(int_operand)
+sum(flux_op(BoundaryPair(int_operand, join_fields(0, bdry_state, *bdry_fluxes), tag))
for tag, bdry_state, bdry_fluxes in bdry_tag_state_flux))
def add_div_bcs(self, tgt, bc_getter, dirichlet_tags, neumann_tags,
stab_term, adjust_flux, flux_v, flux_arg_int,
grad_flux_arg_count):
from pytools.obj_array import make_obj_array, join_fields
n_times = tgt.normal_times_flux
def unwrap_cse(expr):
from pymbolic.primitives import CommonSubexpression
if isinstance(expr, CommonSubexpression):
return expr.child
else:
return expr
for tag in dirichlet_tags:
dir_bc_w = join_fields([0] * grad_flux_arg_count, [
bc_getter(tag, unwrap_cse(vol_expr))
for vol_expr in flux_arg_int[grad_flux_arg_count:]
])
tgt.add_boundary_flux(adjust_flux(n_times(flux_v.int - stab_term)),
flux_arg_int, dir_bc_w, tag)
loc_bc_vec = make_obj_array([0] * len(flux_arg_int))
for tag in neumann_tags:
neu_bc_w = join_fields(
NeumannBCGenerator(tag, bc_getter(tag, None))(tgt.operand),
[0] * len(flux_arg_int))
tgt.add_boundary_flux(adjust_flux(n_times(flux_v.ext)), loc_bc_vec,
neu_bc_w, tag)
def make_lax_friedrichs_flux(wave_speed, state, fluxes, bdry_tags_states_and_fluxes,
strong):
from pytools.obj_array import join_fields
from hedge.flux import make_normal, FluxVectorPlaceholder, flux_max
n = len(state)
d = len(fluxes)
normal = make_normal(d)
fvph = FluxVectorPlaceholder(len(state)*(1+d)+1)
wave_speed_ph = fvph[0]
state_ph = fvph[1:1+n]
fluxes_ph = [fvph[1+i*n:1+(i+1)*n] for i in range(1, d+1)]
penalty = flux_max(wave_speed_ph.int,wave_speed_ph.ext)*(state_ph.ext-state_ph.int)
if not strong:
num_flux = 0.5*(sum(n_i*(f_i.int+f_i.ext) for n_i, f_i in zip(normal, fluxes_ph))
- penalty)
else:
num_flux = 0.5*(sum(n_i*(f_i.int-f_i.ext) for n_i, f_i in zip(normal, fluxes_ph))
+ penalty)
from hedge.optemplate import get_flux_operator
flux_op = get_flux_operator(num_flux)
int_operand = join_fields(wave_speed, state, *fluxes)
from hedge.optemplate import BoundaryPair
return (flux_op(int_operand)
+ sum(
flux_op(BoundaryPair(int_operand,
join_fields(0, bdry_state, *bdry_fluxes), tag))
for tag, bdry_state, bdry_fluxes in bdry_tags_states_and_fluxes))
def add_div_bcs(self, tgt, bc_getter, dirichlet_tags, neumann_tags,
stab_term, adjust_flux, flux_v, flux_arg_int,
grad_flux_arg_count):
from pytools.obj_array import make_obj_array, join_fields
n_times = tgt.normal_times_flux
def unwrap_cse(expr):
from pymbolic.primitives import CommonSubexpression
if isinstance(expr, CommonSubexpression):
return expr.child
else:
return expr
for tag in dirichlet_tags:
dir_bc_w = join_fields(
[0]*grad_flux_arg_count,
[bc_getter(tag, unwrap_cse(vol_expr)) for vol_expr in
flux_arg_int[grad_flux_arg_count:]])
tgt.add_boundary_flux(
adjust_flux(n_times(flux_v.int-stab_term)),
flux_arg_int, dir_bc_w, tag)
loc_bc_vec = make_obj_array([0]*len(flux_arg_int))
for tag in neumann_tags:
neu_bc_w = join_fields(
NeumannBCGenerator(tag, bc_getter(tag, None))(tgt.operand),
[0]*len(flux_arg_int))
tgt.add_boundary_flux(
adjust_flux(n_times(flux_v.ext)),
loc_bc_vec, neu_bc_w, tag)
def op_template(self):
dim = self.dimensions
q = make_vector_field('q', self.len_q)
f2 = make_vector_field('f2', self.len_f2)
w = join_fields(q, f2)
dim_subset = (True,) * dim + (False,) * (3-dim)
def pad_vec(v, subset):
result = numpy.zeros((3,), dtype=object)
result[numpy.array(subset, dtype=bool)] = v
return result
sigma = pad_vec(make_vector_field('sigma', dim),dim_subset)
alpha = pad_vec(make_vector_field('alpha', dim),dim_subset)
kappa = pad_vec(make_vector_field('kappa', dim),dim_subset)
fluxes = self.flux(w, kappa)
# Boundary conditions
q_bc_stressfree = BoundarizeOperator(self.boundaryconditions_tag['stressfree'])(q)
q_bc_stressfree_null = BoundarizeOperator(self.boundaryconditions_tag['stressfree'])(0)
q_bc_fixed = BoundarizeOperator(self.boundaryconditions_tag['fixed'])(q)
q_bc_fixed_null = BoundarizeOperator(self.boundaryconditions_tag['fixed'])(0)
all_tags_and_bcs = [
(self.boundaryconditions_tag['stressfree'], q_bc_stressfree, q_bc_stressfree_null),
(self.boundaryconditions_tag['fixed'], q_bc_fixed, q_bc_fixed_null)
]
bdry_tag_state_flux = [(tag, bc, self.bdry_flux(bc, bc_null, tag))
for tag, bc, bc_null in all_tags_and_bcs]
# Entire operator
nabla = make_nabla(dim)
res_q = (numpy.dot(nabla, fluxes) + InverseMassOperator()
* (self.flux_num(q, fluxes, bdry_tag_state_flux)))
res_q = self.add_sources(res_q)
F2 = self.F2(w)
P = self.P(q)
v = self.v(q)
if dim == 1:
F = [P[0],v[0]]
elif dim == 2:
F = [P[0],P[2],v[0],v[1],
P[2],P[1],v[1],v[0]]
elif dim == 3:
F = [P[0],P[5],P[4],v[0],v[2],v[1],
P[5],P[1],P[3],v[1],v[2],v[0],
P[4],P[3],P[2],v[2],v[1],v[0]]
else:
raise ValueError("Invalid dimension")
res_f2 = numpy.zeros(self.len_f2, dtype=object)
for i in range(dim):
for j in range(dim*2):
res_f2[i*dim*2+j] = (-1)*F2[i*dim*2+j]*alpha[i]-sigma[i]/kappa[i]*(F2[i*dim*2+j]+F[i*dim*2+j])
return join_fields(res_q, res_f2)
def sym_operator(self):
d = self.ambient_dim
w = sym.make_sym_array("w", d + 1)
u = w[0]
v = w[1:]
# boundary conditions -------------------------------------------------
# dirichlet BCs -------------------------------------------------------
dir_u = sym.cse(sym.interp("vol", self.dirichlet_tag)(u))
dir_v = sym.cse(sym.interp("vol", self.dirichlet_tag)(v))
if self.dirichlet_bc_f:
# FIXME
from warnings import warn
warn("Inhomogeneous Dirichlet conditions on the wave equation "
"are still having issues.")
dir_g = sym.Field("dir_bc_u")
dir_bc = join_fields(2 * dir_g - dir_u, dir_v)
else:
dir_bc = join_fields(-dir_u, dir_v)
dir_bc = sym.cse(dir_bc, "dir_bc")
# neumann BCs ---------------------------------------------------------
neu_u = sym.cse(sym.interp("vol", self.neumann_tag)(u))
neu_v = sym.cse(sym.interp("vol", self.neumann_tag)(v))
neu_bc = sym.cse(join_fields(neu_u, -neu_v), "neu_bc")
# radiation BCs -------------------------------------------------------
rad_normal = sym.normal(self.radiation_tag, d)
rad_u = sym.cse(sym.interp("vol", self.radiation_tag)(u))
rad_v = sym.cse(sym.interp("vol", self.radiation_tag)(v))
rad_bc = sym.cse(
join_fields(
0.5 * (rad_u - self.sign * np.dot(rad_normal, rad_v)), 0.5 *
rad_normal * (np.dot(rad_normal, rad_v) - self.sign * rad_u)),
"rad_bc")
# entire operator -----------------------------------------------------
def flux(pair):
return sym.interp(pair.dd, "all_faces")(self.flux(pair))
result = sym.InverseMassOperator()(
join_fields(-self.c *
np.dot(sym.stiffness_t(self.ambient_dim), v), -self.c *
(sym.stiffness_t(self.ambient_dim) * u)) -
sym.FaceMassOperator()
(flux(sym.int_tpair(w)) +
flux(sym.bv_tpair(self.dirichlet_tag, w, dir_bc)) +
flux(sym.bv_tpair(self.neumann_tag, w, neu_bc)) +
flux(sym.bv_tpair(self.radiation_tag, w, rad_bc))))
result[0] += self.source_f
return result
def flux(self, w):
"""The template for the numerical flux for variable coefficients.
:param flux_type: can be in [0,1] for anything between central and upwind,
or "lf" for Lax-Friedrichs.
As per Hesthaven and Warburton page 433.
"""
normal = sym.normal(w.dd, self.dimensions)
if self.fixed_material:
e, h = self.split_eh(w)
epsilon = self.epsilon
mu = self.mu
Z_int = (mu/epsilon)**0.5 # noqa: N806
Y_int = 1/Z_int # noqa: N806
Z_ext = (mu/epsilon)**0.5 # noqa: N806
Y_ext = 1/Z_ext # noqa: N806
if self.flux_type == "lf":
# if self.fixed_material:
# max_c = (self.epsilon*self.mu)**(-0.5)
return join_fields(
# flux e,
1/2*(
-self.space_cross_h(normal, h.int-h.ext)
# multiplication by epsilon undoes material divisor below
#-max_c*(epsilon*e.int - epsilon*e.ext)
),
# flux h
1/2*(
self.space_cross_e(normal, e.int-e.ext)
# multiplication by mu undoes material divisor below
#-max_c*(mu*h.int - mu*h.ext)
))
elif isinstance(self.flux_type, (int, float)):
# see doc/maxima/maxwell.mac
return join_fields(
# flux e,
(
-1/(Z_int+Z_ext)*self.space_cross_h(normal,
Z_ext*(h.int-h.ext)
- self.flux_type*self.space_cross_e(normal, e.int-e.ext))
),
# flux h
(
1/(Y_int + Y_ext)*self.space_cross_e(normal,
Y_ext*(e.int-e.ext)
+ self.flux_type*self.space_cross_h(normal, h.int-h.ext))
),
)
else:
raise ValueError("maxwell: invalid flux_type (%s)"
% self.flux_type)
def __call__(self, x, y, three_mult=None):
"""Compute the subsetted cross product on the indexables *x* and *y*.
:param three_mult: a function of three arguments *sign, xj, yk*
used in place of the product *sign*xj*yk*. Defaults to just this
product if not given.
"""
from pytools.obj_array import join_fields
if three_mult is None:
return join_fields(*[f(x, y) for f in self.functions])
else:
return join_fields(
*[sum(three_mult(lc, x[j], y[k]) for lc, j, k in lcjk)
for lcjk in self.component_lcjk])
def __call__(self, x, y, three_mult=None):
"""Compute the subsetted cross product on the indexables *x* and *y*.
:param three_mult: a function of three arguments *sign, xj, yk*
used in place of the product *sign*xj*yk*. Defaults to just this
product if not given.
"""
from pytools.obj_array import join_fields
if three_mult is None:
return join_fields(*[f(x, y) for f in self.functions])
else:
return join_fields(*[
sum(three_mult(lc, x[j], y[k]) for lc, j, k in lcjk)
for lcjk in self.component_lcjk
])
def flux(self, w):
u = w[0]
v = w[1:]
normal = sym.normal(w.dd, self.ambient_dim)
flux_weak = join_fields(np.dot(v.avg, normal), u.avg * normal)
if self.flux_type == "central":
return -self.c * flux_weak
elif self.flux_type == "upwind":
return -self.c * (flux_weak + self.sign * join_fields(
0.5 * (u.int - u.ext), 0.5 *
(normal * np.dot(normal, v.int - v.ext))))
else:
raise ValueError("invalid flux type '%s'" % self.flux_type)
def noslip_state(self, state):
from hedge.optemplate import make_normal
state0 = join_fields(make_sym_vector("bc_q_noslip", 2),
[0] * self.dimensions)
normal = make_normal(self.noslip_tag, self.dimensions)
bc = self.make_bc_info("bc_q_noslip", self.noslip_tag, state, state0)
return self.inflow_state_inner(normal, bc, "noslip")
def absorbing_bc(self, w):
"""Construct part of the flux operator template for 1st order
absorbing boundary conditions.
"""
absorb_normal = sym.normal(self.absorb_tag, self.dimensions)
e, h = self.split_eh(w)
if self.fixed_material:
epsilon = self.epsilon
mu = self.mu
absorb_Z = (mu/epsilon)**0.5 # noqa: N806
absorb_Y = 1/absorb_Z # noqa: N806
absorb_e = sym.cse(sym.interp("vol", self.absorb_tag)(e))
absorb_h = sym.cse(sym.interp("vol", self.absorb_tag)(h))
bc = join_fields(
absorb_e + 1/2*(self.space_cross_h(absorb_normal, self.space_cross_e(
absorb_normal, absorb_e))
- absorb_Z*self.space_cross_h(absorb_normal, absorb_h)),
absorb_h + 1/2*(
self.space_cross_e(absorb_normal, self.space_cross_h(
absorb_normal, absorb_h))
+ absorb_Y*self.space_cross_e(absorb_normal, absorb_e)))
return bc
def get_spherical_coord(x_vec):
"""
:param x_vec: is an array whose leading dimension iterates over
the X, Y, Z axes, and whose further dimensions may iterate over
a number of points.
:returns: object array of [r, phi, theta].
phi is the angle in (x,y) in :math:`(-\\pi,\\pi)`.
"""
if len(x_vec) != 3:
raise ValueError("only 3-d arrays are supported")
x = x_vec[0]
y = x_vec[1]
z = x_vec[2]
r = numpy.sqrt(x**2 + y**2 + z**2)
from warnings import warn
if (numpy.any(r < numpy.power(10.0, -10.0))):
warn('spherical coordinate transformation ill-defined at r=0')
phi = numpy.arctan2(y, x)
theta = numpy.arccos(z / r)
from pytools.obj_array import join_fields
return join_fields(r, phi, theta)
def integral_equation(self, r_tilde, q_tilde, hvf_coefficients):
fix = 0
if self.invertible:
s_ones = cse(S(0, Ones()), "s_ones")
def inv_rank_one_coeff(u):
return cse(Mean(cse(S(0, cse(S(0, u))))))
r_coeff = inv_rank_one_coeff(r_tilde)
q_coeff = inv_rank_one_coeff(q_tilde)
from pytools.obj_array import join_fields
factors = self.cluster_points()
fix = join_fields(
factors[0] * s_ones * (r_coeff),
factors[1] * Ones() * (q_coeff),
)
return DebyeOperatorBase.integral_equation(self,
r_tilde,
q_tilde,
hvf_coefficients,
fix=fix)
def get_spherical_coord(x_vec):
"""
:param x_vec: is an array whose leading dimension iterates over
the X, Y, Z axes, and whose further dimensions may iterate over
a number of points.
:returns: object array of [r, phi, theta].
phi is the angle in (x,y) in :math:`(-\\pi,\\pi)`.
"""
if len(x_vec) != 3:
raise ValueError("only 3-d arrays are supported")
x = x_vec[0]
y = x_vec[1]
z = x_vec[2]
r = numpy.sqrt(x**2+y**2+z**2)
from warnings import warn
if(numpy.any(r<numpy.power(10.0,-10.0))):
warn('spherical coordinate transformation ill-defined at r=0')
phi = numpy.arctan2(y,x)
theta = numpy.arccos(z/r)
from pytools.obj_array import join_fields
return join_fields(r,phi,theta)
def set_up_stepper(self,
discr,
field_var_name,
sym_rhs,
num_fields,
function_registry=base_function_registry,
exec_mapper_factory=ExecutionMapper):
dt_method = LSRK4MethodBuilder(component_id=field_var_name)
dt_code = dt_method.generate()
self.field_var_name = field_var_name
self.state_name = f"input_{field_var_name}"
# Transcribe the phase.
output_vars, results, yielded_states = transcribe_phase(
dt_code, field_var_name, num_fields, "primary", sym_rhs)
# Build the bound operator for the time integrator.
output_t = results[0]
output_dt = results[1]
output_states = results[2]
output_residuals = results[3]
assert len(output_states) == num_fields
assert len(output_states) == len(output_residuals)
from pytools.obj_array import join_fields
flattened_results = join_fields(output_t, output_dt, *output_states)
self.bound_op = bind(discr,
flattened_results,
function_registry=function_registry,
exec_mapper_factory=exec_mapper_factory)
def pmc_bc(self, w):
"Construct part of the flux operator template for PMC boundary conditions"
e, h = self.split_eh(w)
pmc_e = sym.cse(sym.interp("vol", self.pmc_tag)(e))
pmc_h = sym.cse(sym.interp("vol", self.pmc_tag)(h))
return join_fields(pmc_e, -pmc_h)
def map_numpy_array(self, expr):
if len(expr.shape) != 1:
raise ValueError("only 1D numpy arrays are supported")
from pytools.obj_array import join_fields
return join_fields(*[
self.rec(expr[i])
for i in range(len(expr))])
def wave_operator(discr, c, w):
u = w[0]
v = w[1:]
dir_u = discr.interp("vol", BTAG_ALL, u)
dir_v = discr.interp("vol", BTAG_ALL, v)
dir_bval = join_fields(dir_u, dir_v)
dir_bc = join_fields(-dir_u, dir_v)
return (
-join_fields(-c * discr.div(v), -c * discr.grad(u)) + # noqa: W504
discr.inverse_mass(
discr.face_mass(
wave_flux(discr, c=c, w_tpair=interior_trace_pair(discr, w)) +
wave_flux(
discr, c=c, w_tpair=TracePair(BTAG_ALL, dir_bval, dir_bc)))
))
def noslip_state(self, state):
from hedge.optemplate import make_normal
state0 = join_fields(
make_sym_vector("bc_q_noslip", 2),
[0]*self.dimensions)
normal = make_normal(self.noslip_tag, self.dimensions)
bc = self.make_bc_info("bc_q_noslip", self.noslip_tag, state, state0)
return self.inflow_state_inner(normal, bc, "noslip")
def main():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
target_order = 10
from functools import partial
nelements = 30
qbx_order = 4
from sumpy.kernel import LaplaceKernel
from meshmode.mesh.generation import ( # noqa
ellipse, cloverleaf, starfish, drop, n_gon, qbx_peanut,
make_curve_mesh)
mesh = make_curve_mesh(partial(ellipse, 1),
np.linspace(0, 1, nelements+1),
target_order)
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order))
from pytential.qbx import QBXLayerPotentialSource
qbx = QBXLayerPotentialSource(density_discr, 4*target_order,
qbx_order, fmm_order=False)
from pytools.obj_array import join_fields
sig_sym = sym.var("sig")
knl = LaplaceKernel(2)
op = join_fields(
sym.tangential_derivative(mesh.ambient_dim,
sym.D(knl, sig_sym, qbx_forced_limit=+1)).as_scalar(),
sym.tangential_derivative(mesh.ambient_dim,
sym.D(knl, sig_sym, qbx_forced_limit=-1)).as_scalar(),
)
nodes = density_discr.nodes().with_queue(queue)
angle = cl.clmath.atan2(nodes[1], nodes[0])
n = 10
sig = cl.clmath.sin(n*angle)
dt_sig = n*cl.clmath.cos(n*angle)
res = bind(qbx, op)(queue, sig=sig)
extval = res[0].get()
intval = res[1].get()
pv = 0.5*(extval + intval)
dt_sig_h = dt_sig.get()
import matplotlib.pyplot as pt
pt.plot(extval, label="+num")
pt.plot(pv + dt_sig_h*0.5, label="+ex")
pt.legend(loc="best")
pt.show()
def test_stepper_mem_ops(ctx_factory, use_fusion):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
dims = 2
sym_operator, discr = get_strong_wave_op_with_discr_direct(cl_ctx,
dims=dims,
order=3)
t_start = 0
dt = 0.04
t_end = 0.2
from pytools.obj_array import join_fields
ic = join_fields(discr.zeros(queue),
[discr.zeros(queue) for i in range(discr.dim)])
if not use_fusion:
bound_op = bind(discr,
sym_operator,
exec_mapper_factory=ExecutionMapperWithMemOpCounting)
stepper = RK4TimeStepper(
queue,
discr,
"w",
bound_op,
1 + discr.dim,
get_strong_wave_component,
exec_mapper_factory=ExecutionMapperWithMemOpCounting)
else:
stepper = FusedRK4TimeStepper(
queue,
discr,
"w",
sym_operator,
1 + discr.dim,
get_strong_wave_component,
exec_mapper_factory=ExecutionMapperWithMemOpCounting)
step = 0
nsteps = int(np.ceil((t_end + 1e-9) / dt))
for (_, _, profile_data) in stepper.run(ic,
t_start,
dt,
t_end,
return_profile_data=True):
step += 1
logger.info("step %d/%d", step, nsteps)
logger.info("using fusion? %s", use_fusion)
logger.info("bytes read: %d", profile_data["bytes_read"])
logger.info("bytes written: %d", profile_data["bytes_written"])
logger.info("bytes total: %d",
profile_data["bytes_read"] + profile_data["bytes_written"])
def _bound_op(self, queue, t, *args, profile_data=None):
from pytools.obj_array import join_fields
context = {"t": t, self.field_var_name: join_fields(*args)}
result = self.grudge_bound_op(queue,
profile_data=profile_data,
**context)
if profile_data is not None:
result = result[0]
return result
def conservative_to_primitive(self, q, use_cses=True):
if use_cses:
from hedge.optemplate.primitives import make_common_subexpression as cse
else:
def cse(x, name):
return x
return join_fields(self.rho(q), self.p(q), self.u(q))
def conservative_to_primitive(self, q, use_cses=True):
if use_cses:
from hedge.optemplate.primitives import make_common_subexpression as cse
else:
def cse(x, name): return x
return join_fields(
self.rho(q),
self.p(q),
self.u(q))
def normal(self, where):
bdry_discr = self.get_discr(where)
with cl.CommandQueue(self.cl_context) as queue:
((a, ),
(b, )) = with_queue(queue,
parametrization_derivative(queue, bdry_discr))
nrm = 1 / (a**2 + b**2)**0.5
return without_queue(join_fields(b * nrm, -a * nrm))
def flux(self, w, k):
F2 = self.F2(w) #get F'' from state vector w
q = self.q(w)
P = self.P(q)
v = self.v(q)
v_null = Field('state_null')
dim = self.dimensions
# One entry for each flux direction
if dim == 1:
raise NotImplementedError
#return [cse(join_fields(
# v_null,
# (P[0]+F2[0])/k[0], # flux rho_v
# (v[0]+F2[1])/k[0] # flux F
# ), "x_flux")]
elif dim == 2:
return [cse(join_fields(
v_null, (P[0]+F2[0])/k[0],(P[3]+F2[1])/k[0], # flux rho_v
(v[0]+F2[2])/k[0],v_null,v_null,(v[1]+F2[3])/k[0] # flux F
), "x_flux"),
cse(join_fields(
v_null, (P[2]+F2[4])/k[1],(P[1]+F2[5])/k[1], # flux rho_v
v_null,(v[1]+F2[6])/k[1],(v[0]+F2[7])/k[1],v_null # flux F
), "y_flux")]
elif dim == 3:
raise NotImplementedError
#return [cse(join_fields(
# v_null, (P[0]+F2[0])/k[0],(P[8]+F2[1])/k[0],(P[7]+F2[2])/k[0], # flux rho_v
# (v[0]+F2[3])/k[0],v_null,v_null,v_null,v_null,v_null,v_null,(v[2]+F2[4])/k[0],(v[1]+F2[5])/k[0] # flux F
# ), "x_flux"),
# cse(join_fields(
# v_null, (P[5]+F2[6])/k[1],(P[1]+F2[7])/k[1],(P[6]+F2[8])/k[1], # flux rho_v
# v_null,(v[1]+F2[9])/k[1],v_null,v_null,v_null,(v[0]+F2[10])/k[1],(v[2]+F2[11])/k[1],v_null,v_null # flux F
# ), "y_flux"),
# cse(join_fields(
# v_null, (P[4]+F2[12])/k[2],(P[3]+F2[13])/k[2],(P[2]+F2[14])/k[2], # flux rho_v
# v_null,v_null,(v[2]+F2[15])/k[2],(v[1]+F2[16])/k[2],(v[0]+F2[17])/k[2],v_null,v_null,v_null,v_null # flux F
# ), "z_flux")]
else:
raise ValueError("Invalid dimension")
def flux(self, w):
c = w[0]
u = w[1]
v = w[2:]
normal = sym.normal(w.dd, self.ambient_dim)
if self.flux_type == "central":
return -0.5 * join_fields(
np.dot(v.int * c.int + v.ext * c.ext, normal),
(u.int * c.int + u.ext * c.ext) * normal)
elif self.flux_type == "upwind":
return -0.5 * join_fields(
np.dot(normal, c.ext * v.ext + c.int * v.int) + c.ext * u.ext -
c.int * u.int,
normal * (np.dot(normal, c.ext * v.ext - c.int * v.int) +
c.ext * u.ext + c.int * u.int))
else:
raise ValueError("invalid flux type '%s'" % self.flux_type)
def __call__(self, fields):
from hedge.tools import join_fields
#get conserved fields
rho=self.op.rho(fields)
e=self.op.e(fields)
rho_velocity=self.op.rho_u(fields)
#get primitive fields
#to do
#reset field values to cell average
rhoLim=self.get_average(rho)
eLim=self.get_average(e)
temp=join_fields([self.get_average(rho_vel)
for rho_vel in rho_velocity])
#should do for primitive fields too
return join_fields(rhoLim, eLim, temp)
def __call__(self, fields):
from grudge.tools import join_fields
#get conserved fields
rho=self.op.rho(fields)
e=self.op.e(fields)
rho_velocity=self.op.rho_u(fields)
#get primitive fields
#to do
#reset field values to cell average
rhoLim=self.get_average(rho)
eLim=self.get_average(e)
temp=join_fields([self.get_average(rho_vel)
for rho_vel in rho_velocity])
#should do for primitive fields too
return join_fields(rhoLim, eLim, temp)
def make_field_vector(name, components):
"""Return an object array of *components* subscripted
:class:`Variable` instances.
:param components: The number of components in the vector.
"""
if isinstance(components, int):
components = list(range(components))
from pytools.obj_array import join_fields
vfld = Field(name)
return join_fields(*[vfld.index(i) for i in components])
def flux(self, w):
u = w[0]
v = w[1:]
normal = sym.normal(w.dd, self.ambient_dim)
flux_weak = join_fields(np.dot(v.avg, normal), u.avg * normal)
if self.flux_type == "central":
pass
elif self.flux_type == "upwind":
# see doc/notes/grudge-notes.tm
flux_weak -= self.sign * join_fields(
0.5 * (u.int - u.ext), 0.5 *
(normal * np.dot(normal, v.int - v.ext)))
else:
raise ValueError("invalid flux type '%s'" % self.flux_type)
flux_strong = join_fields(np.dot(v.int, normal),
u.int * normal) - flux_weak
return self.c * flux_strong
def make_sym_vector(name, components):
"""Return an object array of *components* subscripted
:class:`Field` instances.
:param components: The number of components in the vector.
"""
if isinstance(components, int):
components = range(components)
from pytools.obj_array import join_fields
vfld = Variable(name)
return join_fields(*[vfld[i] for i in components])
def wall_state(self, state):
from grudge.symbolic import RestrictToBoundary
bc = RestrictToBoundary(self.wall_tag)(state)
wall_rho = self.rho(bc)
wall_e = self.e(bc) # <3 eve
wall_rho_u = self.rho_u(bc)
from grudge.symbolic import make_normal
normal = make_normal(self.wall_tag, self.dimensions)
return join_fields(
wall_rho, wall_e,
wall_rho_u - 2 * numpy.dot(wall_rho_u, normal) * normal)
def bump(discr, queue, t=0):
source_center = np.array([0.0, 0.05])
source_width = 0.05
source_omega = 3
nodes = discr.volume_discr.nodes().with_queue(queue)
center_dist = join_fields([
nodes[0] - source_center[0],
nodes[1] - source_center[1],
])
return (np.cos(source_omega * t) *
clmath.exp(-np.dot(center_dist, center_dist) / source_width**2))
def wall_state(self, state):
from hedge.optemplate import BoundarizeOperator
bc = BoundarizeOperator(self.wall_tag)(state)
wall_rho = self.rho(bc)
wall_e = self.e(bc) # <3 eve
wall_rho_u = self.rho_u(bc)
from hedge.optemplate import make_normal
normal = make_normal(self.wall_tag, self.dimensions)
return join_fields(
wall_rho, wall_e,
wall_rho_u - 2 * numpy.dot(wall_rho_u, normal) * normal)
def inflow_state_inner(self, normal, bc, name):
# see grudge/doc/maxima/euler.mac
return join_fields(
# bc rho
cse(bc.rho0
+ numpy.dot(normal, bc.dumvec)*bc.rho0/(2*bc.c0) + bc.dpm/(2*bc.c0*bc.c0), "bc_rho_"+name),
# bc p
cse(bc.p0
+ bc.c0*bc.rho0*numpy.dot(normal, bc.dumvec)/2 + bc.dpm/2, "bc_p_"+name),
# bc u
cse(bc.u0
+ normal*numpy.dot(normal, bc.dumvec)/2 + bc.dpm*normal/(2*bc.c0*bc.rho0), "bc_u_"+name))
def inflow_state_inner(self, normal, bc, name):
# see hedge/doc/maxima/euler.mac
return join_fields(
# bc rho
cse(bc.rho0
+ numpy.dot(normal, bc.dumvec)*bc.rho0/(2*bc.c0) + bc.dpm/(2*bc.c0*bc.c0), "bc_rho_"+name),
# bc p
cse(bc.p0
+ bc.c0*bc.rho0*numpy.dot(normal, bc.dumvec)/2 + bc.dpm/2, "bc_p_"+name),
# bc u
cse(bc.u0
+ normal*numpy.dot(normal, bc.dumvec)/2 + bc.dpm*normal/(2*bc.c0*bc.rho0), "bc_u_"+name))
def wall_state(self, state):
from hedge.optemplate import BoundarizeOperator
bc = BoundarizeOperator(self.wall_tag)(state)
wall_rho = self.rho(bc)
wall_e = self.e(bc) # <3 eve
wall_rho_u = self.rho_u(bc)
from hedge.optemplate import make_normal
normal = make_normal(self.wall_tag, self.dimensions)
return join_fields(
wall_rho,
wall_e,
wall_rho_u - 2*numpy.dot(wall_rho_u, normal) * normal)
def primitive_to_conservative(self, prims, use_cses=True):
if not use_cses:
from hedge.optemplate.primitives import make_common_subexpression as cse
else:
def cse(x, name):
return x
rho = prims[0]
p = prims[1]
u = prims[2:]
e = self.equation_of_state.p_to_e(p, rho, u)
return join_fields(rho, cse(e, "e"), cse(rho * u, "rho_u"))
def __init__(self,
queue,
discr,
field_var_name,
grudge_bound_op,
num_fields,
component_getter,
exec_mapper_factory=ExecutionMapper):
"""Arguments:
field_var_name: The name of the simulation variable
grudge_bound_op: The BoundExpression for the right-hand side
num_fields: The number of components in the simulation variable
component_getter: A function, which, given an object array
representing the simulation variable, splits the array into
its components
"""
super().__init__(queue, component_getter)
# Construct sym_rhs to have the effect of replacing the RHS calls in the
# dagrt code with calls of the grudge operator.
from grudge.symbolic.primitives import FunctionSymbol, Variable
call = sym.cse(
FunctionSymbol("grudge_op")(
*((Variable("t", dd=sym.DD_SCALAR), ) + tuple(
Variable(field_var_name, dd=sym.DD_VOLUME)[i]
for i in range(num_fields)))))
from pytools.obj_array import join_fields
sym_rhs = join_fields(*(call[i] for i in range(num_fields)))
self.queue = queue
self.grudge_bound_op = grudge_bound_op
from grudge.function_registry import register_external_function
freg = register_external_function(base_function_registry,
"grudge_op",
implementation=self._bound_op,
dd=sym.DD_VOLUME)
self.set_up_stepper(discr, field_var_name, sym_rhs, num_fields, freg,
exec_mapper_factory)
self.component_getter = component_getter
def primitive_to_conservative(self, prims, use_cses=True):
if not use_cses:
from hedge.optemplate.primitives import make_common_subexpression as cse
else:
def cse(x, name): return x
rho = prims[0]
p = prims[1]
u = prims[2:]
e = self.equation_of_state.p_to_e(p, rho, u)
return join_fields(
rho,
cse(e, "e"),
cse(rho * u, "rho_u"))
def wave_flux(discr, c, w_tpair):
u = w_tpair[0]
v = w_tpair[1:]
normal = with_queue(u.int.queue, discr.normal(w_tpair.where))
flux_weak = join_fields(np.dot(v.avg, normal), normal[0] * u.avg,
normal[1] * u.avg)
# upwind
v_jump = np.dot(normal, v.int - v.ext)
flux_weak -= join_fields(
0.5 * (u.int - u.ext),
0.5 * normal[0] * v_jump,
0.5 * normal[1] * v_jump,
)
flux_strong = join_fields(
np.dot(v.int, normal),
u.int * normal[0],
u.int * normal[1],
) - flux_weak
return discr.interp(w_tpair.where, "all_faces", c * flux_strong)
def make_lax_friedrichs_flux(wave_speed, state, fluxes,
bdry_tags_states_and_fluxes, strong):
from pytools.obj_array import join_fields
from hedge.flux import make_normal, FluxVectorPlaceholder, flux_max
n = len(state)
d = len(fluxes)
normal = make_normal(d)
fvph = FluxVectorPlaceholder(len(state) * (1 + d) + 1)
wave_speed_ph = fvph[0]
state_ph = fvph[1:1 + n]
fluxes_ph = [fvph[1 + i * n:1 + (i + 1) * n] for i in range(1, d + 1)]
penalty = flux_max(wave_speed_ph.int,
wave_speed_ph.ext) * (state_ph.ext - state_ph.int)
if not strong:
num_flux = 0.5 * (sum(n_i * (f_i.int + f_i.ext)
for n_i, f_i in zip(normal, fluxes_ph)) -
penalty)
else:
num_flux = 0.5 * (sum(n_i * (f_i.int - f_i.ext)
for n_i, f_i in zip(normal, fluxes_ph)) +
penalty)
from hedge.optemplate import get_flux_operator
flux_op = get_flux_operator(num_flux)
int_operand = join_fields(wave_speed, state, *fluxes)
from hedge.optemplate import BoundaryPair
return (flux_op(int_operand) + sum(
flux_op(
BoundaryPair(int_operand, join_fields(0, bdry_state, *bdry_fluxes),
tag))
for tag, bdry_state, bdry_fluxes in bdry_tags_states_and_fluxes))
def volume_field_base(self, r, q, j):
k = self.k
grad_phi = grad_S(k, r, 3)
grad_psi = grad_S(k, q, 3)
m = cse(self.m(j), "m")
A = cse(S(k, j), "A")
Q = cse(S(k, m), "Q")
E = 1j * k * A - grad_phi - curl_S_volume(k, m)
H = curl_S_volume(k, j) + 1j * k * Q - grad_psi
from pytools.obj_array import join_fields
return join_fields(E, H)
def volume_field_base(self, r, q, j):
k = self.k
grad_phi = grad_S(k, r, 3)
grad_psi = grad_S(k, q, 3)
m = cse(self.m(j), "m")
A = cse(S(k, j), "A")
Q = cse(S(k, m), "Q")
E = 1j*k*A - grad_phi - curl_S_volume(k, m)
H = curl_S_volume(k, j) + 1j*k*Q - grad_psi
from pytools.obj_array import join_fields
return join_fields(E, H)
def make_sym_vector(name, components, var_factory=None):
"""Return an object array of *components* subscripted
:class:`Variable` (or subclass) instances.
:arg components: The number of components in the vector.
:arg var_factory: The :class:`Variable` subclass to use for instantiating
the scalar variables.
"""
if var_factory is None:
var_factory = Variable
if isinstance(components, int):
components = list(range(components))
from pytools.obj_array import join_fields
vfld = var_factory(name)
return join_fields(*[vfld.index(i) for i in components])
def integral_equation(self, *args, **kwargs):
nxnxE, ndotH = self.boundary_field(*args)
nxnxE = cse(nxnxE, "nxnxE")
fix = kwargs.pop("fix", 0)
if kwargs:
raise TypeError("invalid keyword argument(s)")
from pytools.obj_array import make_obj_array
eh_op = make_obj_array([
2*_debye_S0_surf_div(nxnxE),
-ndotH,
]) + fix
k = self.k
j = cse(self.j(*args), "j")
m = cse(self.m(j), "m")
A = cse(S(k, j), "A")
E_minus_grad_phi = 1j*k*A - curl_S_volume(k, m)
from hellskitchen.fmm import DifferenceKernel
from pytools.obj_array import join_fields
return join_fields(
eh_op,
# FIXME: These are inefficient. They compute a full volume field,
# but only actually use the line part of it.
[
# Grad phi integrated on a loop does not contribute.
LineIntegral(E_minus_grad_phi, a_cycle_name)
for a_cycle_name in self.a_cycle_names
],
[
LineIntegral(
# (E(k) - E(0))/(1jk)
# Grad phi integrated on a loop does not contribute.
(1j*k*A - curl_S_volume(DifferenceKernel(k), m))
/(1j*k),
b_cycle_name)
for b_cycle_name in self.b_cycle_names
]
)
def flux(self, q):
from pytools import delta
return [ # one entry for each flux direction
cse(join_fields(
# flux rho
self.rho_u(q)[i],
# flux E
cse(self.e(q)+self.cse_p(q))*self.cse_u(q)[i],
# flux rho_u
make_obj_array([
self.rho_u(q)[i]*self.cse_u(q)[j]
+ delta(i,j) * self.cse_p(q)
for j in range(self.dimensions)
])
), "%s_flux" % AXES[i])
for i in range(self.dimensions)]
def outflow_state(self, state):
from hedge.optemplate import make_normal
normal = make_normal(self.outflow_tag, self.dimensions)
bc = self.make_bc_info("bc_q_out", self.outflow_tag, state)
# see hedge/doc/maxima/euler.mac
return join_fields(
# bc rho
cse(bc.rho0
+ bc.drhom + numpy.dot(normal, bc.dumvec)*bc.rho0/(2*bc.c0)
- bc.dpm/(2*bc.c0*bc.c0), "bc_rho_outflow"),
# bc p
cse(bc.p0
+ bc.c0*bc.rho0*numpy.dot(normal, bc.dumvec)/2 + bc.dpm/2, "bc_p_outflow"),
# bc u
cse(bc.u0
+ bc.dumvec - normal*numpy.dot(normal, bc.dumvec)/2
+ bc.dpm*normal/(2*bc.c0*bc.rho0), "bc_u_outflow"))
def bdry_flux(self, q_bdry, q_null, tag):
if tag == self.boundaryconditions_tag['stressfree']:
signP = -1
signv = 1
elif tag == self.boundaryconditions_tag['fixed']:
signP = 1
signv = -1
else:
raise ValueError("Invalid boundary conditions")
dim = self.dimensions
P = self.P(q_bdry)
v = self.v(q_bdry)
v_null = q_null
# One entry for each flux direction
if dim == 1:
return [cse(join_fields(
v_null,
signP*P[0], # flux rho_v
signv*v[0] # flux F
), "x_bflux")]
elif dim == 2:
return [cse(join_fields(
v_null, signP*P[0],signP*P[2], # flux rho_v
signv*v[0],v_null,v_null,signv*v[1] # flux F
), "x_bflux"),
cse(join_fields(
v_null, signP*P[2],signP*P[1], # flux rho_v
v_null,signv*v[1],signv*v[0],v_null # flux F
), "y_bflux")]
elif dim == 3:
return [cse(join_fields(
v_null, signP*P[0],signP*P[5],signP*P[4], # flux rho_v
signv*v[0],v_null,v_null,v_null,v_null,v_null,signv*v[2],v_null,signv*v[1] # flux F
), "x_bflux"),
cse(join_fields(
v_null, signP*P[5],signP*P[1],signP*P[3], # flux rho_v
v_null,signv*v[1],v_null,v_null,signv*v[2],v_null,v_null,signv*v[0],v_null # flux F
), "y_bflux"),
cse(join_fields(
v_null, signP*P[4],signP*P[3],signP*P[2], # flux rho_v
v_null,v_null,signv*v[2],signv*v[1],v_null,signv*v[0],v_null,v_null,v_null # flux F
), "z_bflux")]
else:
raise ValueError("Invalid dimension")
def make_second_order_part(self):
state = self.state()
faceq_state = self.faceq_state()
volq_state = self.volq_state()
volq_tau_mat = self.tau(to_vol_quad, state)
faceq_tau_mat = self.tau(to_int_face_quad, state)
return join_fields(
0,
self.div(
numpy.sum(volq_tau_mat*self.cse_u(volq_state), axis=1)
+ self.heat_conduction_grad(to_vol_quad)
,
numpy.sum(faceq_tau_mat*self.cse_u(faceq_state), axis=1)
+ self.heat_conduction_grad(to_int_face_quad)
,
),
[
self.div(volq_tau_mat[i], faceq_tau_mat[i])
for i in range(self.dimensions)]
)
def integral_equation(self, r_tilde, q_tilde, hvf_coefficients):
fix = 0
if self.invertible:
s_ones = cse(S(0, Ones()), "s_ones")
def inv_rank_one_coeff(u):
return cse(Mean(cse(S(0, cse(S(0, u))))))
r_coeff = inv_rank_one_coeff(r_tilde)
q_coeff = inv_rank_one_coeff(q_tilde)
from pytools.obj_array import join_fields
factors = self.cluster_points()
fix = join_fields(
factors[0]*s_ones*(r_coeff),
factors[1]*Ones()*(q_coeff),
)
return DebyeOperatorBase.integral_equation(
self, r_tilde, q_tilde, hvf_coefficients, fix=fix)
def flux(self, q):
P = self.P(q)
v = self.v(q)
v_null = Field('state_null')
dim = self.dimensions
# One entry for each flux direction
if dim == 1:
return [cse(join_fields(
v_null,
P[0], # flux rho_v
v[0] # flux F
), "x_flux")]
elif dim == 2:
return [cse(join_fields(
v_null, P[0],P[2],# flux rho_v
v[0],v_null,v[1] # flux F
), "x_flux"),
cse(join_fields(
v_null, P[2],P[1],# flux rho_v
v_null,v[1],v[0] # flux F
), "y_flux")]
elif dim == 3:
return [cse(join_fields(
v_null, P[0],P[5],P[4], # flux rho_v
v[0],v_null,v_null,v_null,v[2],v[1] # flux F
), "x_flux"),
cse(join_fields(
v_null, P[5],P[1],P[3], # flux rho_v
v_null,v[1],v_null,v[2],v_null,v[0] # flux F
), "y_flux"),
cse(join_fields(
v_null, P[4],P[3],P[2], # flux rho_v
v_null,v_null,v[2],v[1],v[0],v_null # flux F
), "z_flux")]
else:
raise ValueError("Invalid dimension")
def op_template(self, sensor_scaling=None, viscosity_only=False):
u = self.cse_u
rho = self.cse_rho
rho_u = self.rho_u
p = self.p
e = self.e
# {{{ artificial diffusion
def make_artificial_diffusion():
if self.artificial_viscosity_mode not in ["diffusion"]:
return 0
dq = self.grad_of_state()
return make_obj_array([
self.div(
to_vol_quad(self.sensor())*to_vol_quad(dq[i]),
to_int_face_quad(self.sensor())*to_int_face_quad(dq[i]))
for i in range(dq.shape[0])])
# }}}
# {{{ state setup
volq_flux = self.flux(self.volq_state())
faceq_flux = self.flux(self.faceq_state())
from hedge.optemplate.primitives import CFunction
sqrt = CFunction("sqrt")
speed = self.characteristic_velocity_optemplate(self.state())
has_viscosity = not is_zero(self.get_mu(self.state(), to_quad_op=None))
# }}}
# {{{ operator assembly -----------------------------------------------
from hedge.flux.tools import make_lax_friedrichs_flux
from hedge.optemplate.operators import InverseMassOperator
from hedge.optemplate.tools import make_stiffness_t
primitive_bcs_as_quad_conservative = dict(
(tag, self.primitive_to_conservative(to_bdry_quad(bc)))
for tag, bc in
self.get_primitive_boundary_conditions().iteritems())
def get_bc_tuple(tag):
state = self.state()
bc = make_obj_array([
self.get_boundary_condition_for(tag, s_i) for s_i in state])
return tag, bc, self.flux(bc)
first_order_part = InverseMassOperator()(
numpy.dot(make_stiffness_t(self.dimensions), volq_flux)
- make_lax_friedrichs_flux(
wave_speed=cse(to_int_face_quad(speed), "emax_c"),
state=self.faceq_state(), fluxes=faceq_flux,
bdry_tags_states_and_fluxes=[
get_bc_tuple(tag) for tag in self.get_boundary_tags()],
strong=False))
if viscosity_only:
first_order_part = 0*first_order_part
result = join_fields(
first_order_part
+ self.make_second_order_part()
+ make_artificial_diffusion()
+ self.make_extra_terms(),
speed)
if self.source is not None:
result = result + join_fields(
make_sym_vector("source_vect", len(self.state())),
# extra field for speed
0)
return result