def main(write_output=True) :
from math import sin, cos, pi, exp, sqrt
from grudge.data import TimeConstantGivenFunction, \
ConstantGivenFunction
from grudge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
def boundary_tagger(fvi, el, fn, all_v):
if el.face_normals[fn][0] > 0:
return ["dirichlet"]
else:
return ["neumann"]
if dim == 2:
if rcon.is_head_rank:
from grudge.mesh.generator import make_disk_mesh
mesh = make_disk_mesh(r=0.5, boundary_tagger=boundary_tagger)
elif dim == 3:
if rcon.is_head_rank:
from grudge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.001)
else:
raise RuntimeError("bad number of dimensions")
if rcon.is_head_rank:
print("%d elements" % len(mesh.elements))
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=3,
debug=["cuda_no_plan"],
default_scalar_type=numpy.float64)
if write_output:
from grudge.visualization import VtkVisualizer
vis = VtkVisualizer(discr, rcon, "fld")
def u0(x, el):
if la.norm(x) < 0.2:
return 1
else:
return 0
def coeff(x, el):
if x[0] < 0:
return 0.25
else:
return 1
def dirichlet_bc(t, x):
return 0
def neumann_bc(t, x):
return 2
from grudge.models.diffusion import DiffusionOperator
op = DiffusionOperator(discr.dimensions,
#coeff=coeff,
dirichlet_tag="dirichlet",
dirichlet_bc=TimeConstantGivenFunction(ConstantGivenFunction(0)),
neumann_tag="neumann",
neumann_bc=TimeConstantGivenFunction(ConstantGivenFunction(1))
)
u = discr.interpolate_volume_function(u0)
# diagnostics setup -------------------------------------------------------
from logpyle import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "heat.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
from grudge.log import LpNorm
u_getter = lambda: u
logmgr.add_quantity(LpNorm(u_getter, discr, 1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# timestep loop -----------------------------------------------------------
from grudge.timestep.runge_kutta import LSRK4TimeStepper, ODE45TimeStepper
from grudge.timestep.dumka3 import Dumka3TimeStepper
#stepper = LSRK4TimeStepper()
stepper = Dumka3TimeStepper(3, rtol=1e-6, rcon=rcon,
vector_primitive_factory=discr.get_vector_primitive_factory(),
dtype=discr.default_scalar_type)
#stepper = ODE45TimeStepper(rtol=1e-6, rcon=rcon,
#vector_primitive_factory=discr.get_vector_primitive_factory(),
#dtype=discr.default_scalar_type)
stepper.add_instrumentation(logmgr)
rhs = op.bind(discr)
try:
next_dt = op.estimate_timestep(discr,
stepper=LSRK4TimeStepper(), t=0, fields=u)
from grudge.timestep import times_and_steps
step_it = times_and_steps(
final_time=0.1, logmgr=logmgr,
max_dt_getter=lambda t: next_dt,
taken_dt_getter=lambda: taken_dt)
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, [
("u", discr.convert_volume(u, kind="numpy")),
], time=t, step=step)
visf.close()
u, t, taken_dt, next_dt = stepper(u, t, next_dt, rhs)
#u = stepper(u, t, dt, rhs)
assert discr.norm(u) < 1
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True):
from grudge.data import GivenFunction, ConstantGivenFunction
from grudge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
def boundary_tagger(fvi, el, fn, points):
from math import atan2, pi
normal = el.face_normals[fn]
if -90/180*pi < atan2(normal[1], normal[0]) < 90/180*pi:
return ["neumann"]
else:
return ["dirichlet"]
def dirichlet_boundary_tagger(fvi, el, fn, points):
return ["dirichlet"]
if dim == 2:
if rcon.is_head_rank:
from grudge.mesh.generator import make_disk_mesh
mesh = make_disk_mesh(r=0.5,
boundary_tagger=dirichlet_boundary_tagger,
max_area=1e-3)
elif dim == 3:
if rcon.is_head_rank:
from grudge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.0001,
boundary_tagger=lambda fvi, el, fn, points:
["dirichlet"])
else:
raise RuntimeError("bad number of dimensions")
if rcon.is_head_rank:
print("%d elements" % len(mesh.elements))
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=5,
debug=[])
def dirichlet_bc(x, el):
from math import sin
return sin(10*x[0])
def rhs_c(x, el):
if la.norm(x) < 0.1:
return 1000
else:
return 0
def my_diff_tensor():
result = numpy.eye(dim)
result[0,0] = 0.1
return result
try:
from grudge.models.poisson import (
PoissonOperator,
HelmholtzOperator)
from grudge.second_order import \
IPDGSecondDerivative, LDGSecondDerivative, \
StabilizedCentralSecondDerivative
k = 1
from grudge.mesh import BTAG_NONE, BTAG_ALL
op = HelmholtzOperator(k, discr.dimensions,
#diffusion_tensor=my_diff_tensor(),
#dirichlet_tag="dirichlet",
#neumann_tag="neumann",
dirichlet_tag=BTAG_ALL,
neumann_tag=BTAG_NONE,
#dirichlet_tag=BTAG_ALL,
#neumann_tag=BTAG_NONE,
#dirichlet_bc=GivenFunction(dirichlet_bc),
dirichlet_bc=ConstantGivenFunction(0),
neumann_bc=ConstantGivenFunction(-10),
scheme=StabilizedCentralSecondDerivative(),
#scheme=LDGSecondDerivative(),
#scheme=IPDGSecondDerivative(),
)
bound_op = op.bind(discr)
if False:
from grudge.iterative import parallel_cg
u = -parallel_cg(rcon, -bound_op,
bound_op.prepare_rhs(discr.interpolate_volume_function(rhs_c)),
debug=20, tol=5e-4,
dot=discr.nodewise_dot_product,
x=discr.volume_zeros())
else:
rhs = bound_op.prepare_rhs(discr.interpolate_volume_function(rhs_c))
def compute_resid(x):
return bound_op(x)-rhs
from scipy.sparse.linalg import minres, LinearOperator
u, info = minres(
LinearOperator(
(len(discr), len(discr)),
matvec=bound_op, dtype=bound_op.dtype),
rhs,
callback=ResidualPrinter(compute_resid),
tol=1e-5)
print()
if info != 0:
raise RuntimeError("gmres reported error %d" % info)
print("finished gmres")
print(la.norm(bound_op(u)-rhs)/la.norm(rhs))
if write_output:
from grudge.visualization import SiloVisualizer, VtkVisualizer
vis = VtkVisualizer(discr, rcon)
visf = vis.make_file("fld")
vis.add_data(visf, [ ("sol", discr.convert_volume(u, kind="numpy")), ])
visf.close()
finally:
discr.close()