def test_efield_vs_gauss_law():
from hedge.mesh.generator import \
make_box_mesh, \
make_cylinder_mesh
from math import sqrt, pi
from pytools.arithmetic_container import \
ArithmeticList, join_fields
from random import seed
from pytools.stopwatch import Job
from pyrticle.units import SIUnitsWithNaturalConstants
units = SIUnitsWithNaturalConstants()
seed(0)
nparticles = 10000
beam_radius = 2.5 * units.MM
emittance = 5 * units.MM * units.MRAD
final_time = 0.1 * units.M / units.VACUUM_LIGHT_SPEED()
field_dump_interval = 1
tube_length = 20 * units.MM
# discretization setup ----------------------------------------------------
from pyrticle.geometry import make_cylinder_with_fine_core
mesh = make_cylinder_with_fine_core(
r=10 * beam_radius,
inner_r=1 * beam_radius,
min_z=0,
max_z=tube_length,
max_volume_inner=10 * units.MM**3,
max_volume_outer=100 * units.MM**3,
radial_subdiv=10,
)
from hedge.backends import guess_run_context
rcon = guess_run_context([])
discr = rcon.make_discretization(mesh, order=3)
from hedge.models.em import MaxwellOperator
max_op = MaxwellOperator(epsilon=units.EPSILON0, mu=units.MU0, flux_type=1)
from hedge.models.nd_calculus import DivergenceOperator
div_op = DivergenceOperator(discr.dimensions)
# particles setup ---------------------------------------------------------
from pyrticle.cloud import PicMethod
from pyrticle.deposition.shape import ShapeFunctionDepositor
from pyrticle.pusher import MonomialParticlePusher
method = PicMethod(discr, units, ShapeFunctionDepositor(),
MonomialParticlePusher(), 3, 3)
# particle ic ---------------------------------------------------------
cloud_charge = -1e-9 * units.C
electrons_per_particle = abs(cloud_charge / nparticles / units.EL_CHARGE)
el_energy = 10 * units.EL_REST_ENERGY()
el_lorentz_gamma = el_energy / units.EL_REST_ENERGY()
beta = (1 - 1 / el_lorentz_gamma**2)**0.5
gamma = 1 / sqrt(1 - beta**2)
from pyrticle.distribution import KVZIntervalBeam
beam = KVZIntervalBeam(units,
total_charge=cloud_charge,
p_charge=cloud_charge / nparticles,
p_mass=electrons_per_particle * units.EL_MASS,
radii=2 * [beam_radius],
emittances=2 * [5 * units.MM * units.MRAD],
z_length=tube_length,
z_pos=tube_length / 2,
beta=beta)
state = method.make_state()
method.add_particles(state, beam.generate_particles(), nparticles)
# field ic ----------------------------------------------------------------
from pyrticle.cloud import guess_shape_bandwidth
guess_shape_bandwidth(method, state, 2)
from pyrticle.cloud import compute_initial_condition
from hedge.data import ConstantGivenFunction
fields = compute_initial_condition(rcon,
discr,
method,
state,
maxwell_op=max_op,
potential_bc=ConstantGivenFunction())
# check against theory ----------------------------------------------------
q_per_unit_z = cloud_charge / beam.z_length
class TheoreticalEField:
shape = (3, )
def __call__(self, x, el):
r = la.norm(x[:2])
if r >= max(beam.radii):
xy_unit = x / r
xy_unit[2] = 0
return xy_unit * ((q_per_unit_z) /
(2 * pi * r * max_op.epsilon))
else:
return numpy.zeros((3, ))
def theory_indicator(x, el):
r = la.norm(x[:2])
if r >= max(beam.radii):
return 1
else:
return 0
from hedge.tools import join_fields, to_obj_array
e_theory = to_obj_array(
discr.interpolate_volume_function(TheoreticalEField()))
theory_ind = discr.interpolate_volume_function(theory_indicator)
e_field, h_field = max_op.split_eh(fields)
restricted_e = join_fields(*[e_i * theory_ind for e_i in e_field])
def l2_error(field, true):
return discr.norm(field - true) / discr.norm(true)
outer_l2 = l2_error(restricted_e, e_theory)
assert outer_l2 < 0.08
if False:
visf = vis.make_file("e_comparison")
mesh_scalars, mesh_vectors = \
method.add_to_vis(vis, visf)
vis.add_data(visf, [
("e", restricted_e),
("e_theory", e_theory),
] + mesh_vectors + mesh_scalars)
visf.close()
def main(write_output=True, allow_features=None, flux_type_arg=1, bdry_flux_type_arg=None, extra_discr_args={}):
from hedge.mesh.generator import make_cylinder_mesh, make_box_mesh
from hedge.tools import EOCRecorder, to_obj_array
from math import sqrt, pi
from analytic_solutions import (
check_time_harmonic_solution,
RealPartAdapter,
SplitComplexAdapter,
CylindricalFieldAdapter,
CylindricalCavityMode,
RectangularWaveguideMode,
RectangularCavityMode,
)
from hedge.models.em import MaxwellOperator
from hedge.backends import guess_run_context
rcon = guess_run_context(allow_features)
epsilon0 = 8.8541878176e-12 # C**2 / (N m**2)
mu0 = 4 * pi * 1e-7 # N/A**2.
epsilon = 1 * epsilon0
mu = 1 * mu0
eoc_rec = EOCRecorder()
cylindrical = False
periodic = False
if cylindrical:
R = 1
d = 2
mode = CylindricalCavityMode(m=1, n=1, p=1, radius=R, height=d, epsilon=epsilon, mu=mu)
r_sol = CylindricalFieldAdapter(RealPartAdapter(mode))
c_sol = SplitComplexAdapter(CylindricalFieldAdapter(mode))
if rcon.is_head_rank:
mesh = make_cylinder_mesh(radius=R, height=d, max_volume=0.01)
else:
if periodic:
mode = RectangularWaveguideMode(epsilon, mu, (3, 2, 1))
periodicity = (False, False, True)
else:
periodicity = None
mode = RectangularCavityMode(epsilon, mu, (1, 2, 2))
if rcon.is_head_rank:
mesh = make_box_mesh(max_volume=0.001, periodicity=periodicity)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [4, 5, 6]:
# for order in [1,2,3,4,5,6]:
extra_discr_args.setdefault("debug", []).extend(["cuda_no_plan", "cuda_dump_kernels"])
op = MaxwellOperator(epsilon, mu, flux_type=flux_type_arg, bdry_flux_type=bdry_flux_type_arg)
discr = rcon.make_discretization(mesh_data, order=order, tune_for=op.op_template(), **extra_discr_args)
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "em-%d" % order)
mode.set_time(0)
def get_true_field():
return discr.convert_volume(
to_obj_array(mode(discr).real.astype(discr.default_scalar_type).copy()), kind=discr.compute_kind
)
fields = get_true_field()
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(dtype=discr.default_scalar_type, rcon=rcon)
# from hedge.timestep.dumka3 import Dumka3TimeStepper
# stepper = Dumka3TimeStepper(3, dtype=discr.default_scalar_type, rcon=rcon)
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, add_simulation_quantities, add_run_info
if write_output:
log_file_name = "maxwell-%d.dat" % order
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)
stepper.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
from hedge.log import EMFieldGetter, add_em_quantities
field_getter = EMFieldGetter(discr, op, lambda: fields)
add_em_quantities(logmgr, op, field_getter)
logmgr.add_watches(["step.max", "t_sim.max", ("W_field", "W_el+W_mag"), "t_step.max"])
# timestep loop -------------------------------------------------------
rhs = op.bind(discr)
final_time = 0.5e-9
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=final_time,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr, stepper=stepper, t=t, fields=fields),
)
for step, t, dt in step_it:
if step % 50 == 0 and write_output:
sub_timer = vis_timer.start_sub_timer()
e, h = op.split_eh(fields)
visf = vis.make_file("em-%d-%04d" % (order, step))
vis.add_data(
visf,
[("e", discr.convert_volume(e, kind="numpy")), ("h", discr.convert_volume(h, kind="numpy"))],
time=t,
step=step,
)
visf.close()
sub_timer.stop().submit()
fields = stepper(fields, t, dt, rhs)
mode.set_time(final_time)
eoc_rec.add_data_point(order, discr.norm(fields - get_true_field()))
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
if rcon.is_head_rank:
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
assert eoc_rec.estimate_order_of_convergence()[0, 1] > 6
def test_efield_vs_gauss_law():
from hedge.mesh.generator import \
make_box_mesh, \
make_cylinder_mesh
from math import sqrt, pi
from pytools.arithmetic_container import \
ArithmeticList, join_fields
from random import seed
from pytools.stopwatch import Job
from pyrticle.units import SIUnitsWithNaturalConstants
units = SIUnitsWithNaturalConstants()
seed(0)
nparticles = 10000
beam_radius = 2.5 * units.MM
emittance = 5 * units.MM * units.MRAD
final_time = 0.1*units.M/units.VACUUM_LIGHT_SPEED()
field_dump_interval = 1
tube_length = 20*units.MM
# discretization setup ----------------------------------------------------
from pyrticle.geometry import make_cylinder_with_fine_core
mesh = make_cylinder_with_fine_core(
r=10*beam_radius, inner_r=1*beam_radius,
min_z=0, max_z=tube_length,
max_volume_inner=10*units.MM**3,
max_volume_outer=100*units.MM**3,
radial_subdiv=10,
)
from hedge.backends import guess_run_context
rcon = guess_run_context([])
discr = rcon.make_discretization(mesh, order=3)
from hedge.models.em import MaxwellOperator
max_op = MaxwellOperator(
epsilon=units.EPSILON0,
mu=units.MU0,
flux_type=1)
from hedge.models.nd_calculus import DivergenceOperator
div_op = DivergenceOperator(discr.dimensions)
# particles setup ---------------------------------------------------------
from pyrticle.cloud import PicMethod
from pyrticle.deposition.shape import ShapeFunctionDepositor
from pyrticle.pusher import MonomialParticlePusher
method = PicMethod(discr, units,
ShapeFunctionDepositor(),
MonomialParticlePusher(),
3, 3)
# particle ic ---------------------------------------------------------
cloud_charge = -1e-9 * units.C
electrons_per_particle = abs(cloud_charge/nparticles/units.EL_CHARGE)
el_energy = 10*units.EL_REST_ENERGY()
el_lorentz_gamma = el_energy/units.EL_REST_ENERGY()
beta = (1-1/el_lorentz_gamma**2)**0.5
gamma = 1/sqrt(1-beta**2)
from pyrticle.distribution import KVZIntervalBeam
beam = KVZIntervalBeam(units, total_charge=cloud_charge,
p_charge=cloud_charge/nparticles,
p_mass=electrons_per_particle*units.EL_MASS,
radii=2*[beam_radius],
emittances=2*[5 * units.MM * units.MRAD],
z_length=tube_length,
z_pos=tube_length/2,
beta=beta)
state = method.make_state()
method.add_particles(state, beam.generate_particles(), nparticles)
# field ic ----------------------------------------------------------------
from pyrticle.cloud import guess_shape_bandwidth
guess_shape_bandwidth(method, state, 2)
from pyrticle.cloud import compute_initial_condition
from hedge.data import ConstantGivenFunction
fields = compute_initial_condition(
rcon,
discr, method, state, maxwell_op=max_op,
potential_bc=ConstantGivenFunction())
# check against theory ----------------------------------------------------
q_per_unit_z = cloud_charge/beam.z_length
class TheoreticalEField:
shape = (3,)
def __call__(self, x, el):
r = la.norm(x[:2])
if r >= max(beam.radii):
xy_unit = x/r
xy_unit[2] = 0
return xy_unit*((q_per_unit_z)
/
(2*pi*r*max_op.epsilon))
else:
return numpy.zeros((3,))
def theory_indicator(x, el):
r = la.norm(x[:2])
if r >= max(beam.radii):
return 1
else:
return 0
from hedge.tools import join_fields, to_obj_array
e_theory = to_obj_array(discr.interpolate_volume_function(TheoreticalEField()))
theory_ind = discr.interpolate_volume_function(theory_indicator)
e_field, h_field = max_op.split_eh(fields)
restricted_e = join_fields(*[e_i * theory_ind for e_i in e_field])
def l2_error(field, true):
return discr.norm(field-true)/discr.norm(true)
outer_l2 = l2_error(restricted_e, e_theory)
assert outer_l2 < 0.08
if False:
visf = vis.make_file("e_comparison")
mesh_scalars, mesh_vectors = \
method.add_to_vis(vis, visf)
vis.add_data(visf, [
("e", restricted_e),
("e_theory", e_theory),
]
+ mesh_vectors
+ mesh_scalars
)
visf.close()
def main(write_output=True,
allow_features=None,
flux_type_arg=1,
bdry_flux_type_arg=None,
extra_discr_args={}):
from hedge.mesh.generator import make_cylinder_mesh, make_box_mesh
from hedge.tools import EOCRecorder, to_obj_array
from math import sqrt, pi # noqa
from analytic_solutions import ( # noqa
RealPartAdapter, SplitComplexAdapter, CylindricalFieldAdapter,
CylindricalCavityMode, RectangularWaveguideMode, RectangularCavityMode)
from hedge.models.em import MaxwellOperator
logging.basicConfig(level=logging.DEBUG)
from hedge.backends import guess_run_context
rcon = guess_run_context(allow_features)
epsilon0 = 8.8541878176e-12 # C**2 / (N m**2)
mu0 = 4 * pi * 1e-7 # N/A**2.
epsilon = 1 * epsilon0
mu = 1 * mu0
eoc_rec = EOCRecorder()
cylindrical = False
periodic = False
if cylindrical:
R = 1
d = 2
mode = CylindricalCavityMode(m=1,
n=1,
p=1,
radius=R,
height=d,
epsilon=epsilon,
mu=mu)
# r_sol = CylindricalFieldAdapter(RealPartAdapter(mode))
# c_sol = SplitComplexAdapter(CylindricalFieldAdapter(mode))
if rcon.is_head_rank:
mesh = make_cylinder_mesh(radius=R, height=d, max_volume=0.01)
else:
if periodic:
mode = RectangularWaveguideMode(epsilon, mu, (3, 2, 1))
periodicity = (False, False, True)
else:
periodicity = None
mode = RectangularCavityMode(epsilon, mu, (1, 2, 2))
if rcon.is_head_rank:
mesh = make_box_mesh(max_volume=0.001, periodicity=periodicity)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [4, 5, 6]:
#for order in [1,2,3,4,5,6]:
extra_discr_args.setdefault("debug", []).extend(
["cuda_no_plan", "cuda_dump_kernels"])
op = MaxwellOperator(epsilon,
mu,
flux_type=flux_type_arg,
bdry_flux_type=bdry_flux_type_arg)
discr = rcon.make_discretization(mesh_data,
order=order,
tune_for=op.op_template(),
**extra_discr_args)
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "em-%d" % order)
mode.set_time(0)
def get_true_field():
return discr.convert_volume(to_obj_array(
mode(discr).real.astype(discr.default_scalar_type).copy()),
kind=discr.compute_kind)
fields = get_true_field()
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(dtype=discr.default_scalar_type, rcon=rcon)
#from hedge.timestep.dumka3 import Dumka3TimeStepper
#stepper = Dumka3TimeStepper(3, dtype=discr.default_scalar_type, rcon=rcon)
# {{{ diagnostics setup
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_file_name = "maxwell-%d.dat" % order
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)
stepper.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
from hedge.log import EMFieldGetter, add_em_quantities
field_getter = EMFieldGetter(discr, op, lambda: fields)
add_em_quantities(logmgr, op, field_getter)
logmgr.add_watches(
["step.max", "t_sim.max", ("W_field", "W_el+W_mag"), "t_step.max"])
# }}}
# {{{ timestep loop
rhs = op.bind(discr)
final_time = 0.5e-9
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=final_time,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
if step % 50 == 0 and write_output:
sub_timer = vis_timer.start_sub_timer()
e, h = op.split_eh(fields)
visf = vis.make_file("em-%d-%04d" % (order, step))
vis.add_data(visf, [
("e", discr.convert_volume(e, kind="numpy")),
("h", discr.convert_volume(h, kind="numpy")),
],
time=t,
step=step)
visf.close()
sub_timer.stop().submit()
fields = stepper(fields, t, dt, rhs)
mode.set_time(final_time)
eoc_rec.add_data_point(order,
discr.norm(fields - get_true_field()))
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
if rcon.is_head_rank:
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
# }}}
assert eoc_rec.estimate_order_of_convergence()[0, 1] > 6
