def test_kv_with_no_charge():
from random import seed
seed(0)
from pyrticle.units import SIUnitsWithNaturalConstants
units = SIUnitsWithNaturalConstants()
# discretization setup ----------------------------------------------------
from hedge.mesh import make_cylinder_mesh
from hedge.backends import guess_run_context
rcon = guess_run_context([])
tube_length = 100 * units.MM
mesh = make_cylinder_mesh(radius=25 * units.MM,
height=tube_length,
periodic=True)
discr = rcon.make_discretization(mesh, order=3)
dt = discr.dt_factor(units.VACUUM_LIGHT_SPEED()) / 2
final_time = 1 * units.M / units.VACUUM_LIGHT_SPEED()
nsteps = int(final_time / dt) + 1
dt = final_time / nsteps
# 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)
nparticles = 10000
cloud_charge = 1e-9 * units.C
electrons_per_particle = cloud_charge / nparticles / units.EL_CHARGE
el_energy = 5.2e6 * units.EV
gamma = el_energy / units.EL_REST_ENERGY()
beta = (1 - 1 / gamma**2)**0.5
from pyrticle.distribution import KVZIntervalBeam
beam = KVZIntervalBeam(units,
total_charge=0,
p_charge=0,
p_mass=electrons_per_particle * units.EL_MASS,
radii=2 * [2.5 * units.MM],
emittances=2 * [5 * units.MM * units.MRAD],
z_length=5 * units.MM,
z_pos=10 * units.MM,
beta=beta)
state = method.make_state()
method.add_particles(state, beam.generate_particles(), nparticles)
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager
from pyrticle.log import add_beam_quantities, StateObserver
observer = StateObserver(method, None)
logmgr = LogManager(mode="w")
add_beam_quantities(logmgr, observer, axis=0, beam_axis=2)
from pyrticle.distribution import KVPredictedRadius
logmgr.add_quantity(
KVPredictedRadius(dt,
beam_v=beta * units.VACUUM_LIGHT_SPEED(),
predictor=beam.get_rms_predictor(axis=0),
suffix="x_rms"))
logmgr.add_quantity(
KVPredictedRadius(dt,
beam_v=beta * units.VACUUM_LIGHT_SPEED(),
predictor=beam.get_total_predictor(axis=0),
suffix="x_total"))
# timestep loop -----------------------------------------------------------
vel = method.velocities(state)
from hedge.tools import join_fields
def rhs(t, y):
return join_fields([
vel,
0 * vel,
0, # drecon
])
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
t = 0
from pyrticle.cloud import TimesteppablePicState
ts_state = TimesteppablePicState(method, state)
for step in xrange(nsteps):
observer.set_fields_and_state(None, ts_state.state)
logmgr.tick()
ts_state = stepper(ts_state, t, dt, rhs)
method.upkeep(ts_state.state)
t += dt
logmgr.tick()
_, _, err_table = logmgr.get_expr_dataset(
"(rx_rms-rx_rms_theory)/rx_rms_theory")
rel_max_rms_error = max(err for step, err in err_table)
assert rel_max_rms_error < 0.01
def main(write_output=True):
from hedge.timestep import RK4TimeStepper
from hedge.mesh import make_disk_mesh
from math import sqrt, pi, exp
from hedge.backends import guess_run_context, FEAT_CUDA
rcon = guess_run_context()
epsilon0 = 8.8541878176e-12 # C**2 / (N m**2)
mu0 = 4*pi*1e-7 # N/A**2.
epsilon = 1*epsilon0
mu = 1*mu0
c = 1/sqrt(mu*epsilon)
cylindrical = False
periodic = False
pml_width = 0.5
#mesh = make_mesh(a=numpy.array((-1,-1,-1)), b=numpy.array((1,1,1)),
#mesh = make_mesh(a=numpy.array((-3,-3)), b=numpy.array((3,3)),
mesh = make_mesh(a=numpy.array((-1,-1)), b=numpy.array((1,1)),
#mesh = make_mesh(a=numpy.array((-2,-2)), b=numpy.array((2,2)),
pml_width=pml_width, max_volume=0.01)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
class Current:
def volume_interpolant(self, t, discr):
from hedge.tools import make_obj_array
result = discr.volume_zeros(kind="numpy", dtype=numpy.float64)
omega = 6*c
if omega*t > 2*pi:
return make_obj_array([result, result, result])
x = make_obj_array(discr.nodes.T)
r = numpy.sqrt(numpy.dot(x, x))
idx = r<0.3
result[idx] = (1+numpy.cos(pi*r/0.3))[idx] \
*numpy.sin(omega*t)**3
result = discr.convert_volume(result, kind=discr.compute_kind,
dtype=discr.default_scalar_type)
return make_obj_array([-result, result, result])
order = 3
discr = rcon.make_discretization(mesh_data, order=order,
debug=["cuda_no_plan"])
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "em-%d" % order)
from hedge.mesh import TAG_ALL, TAG_NONE
from hedge.data import GivenFunction, TimeHarmonicGivenFunction, TimeIntervalGivenFunction
from hedge.models.em import MaxwellOperator
from hedge.models.pml import \
AbarbanelGottliebPMLMaxwellOperator, \
AbarbanelGottliebPMLTMMaxwellOperator, \
AbarbanelGottliebPMLTEMaxwellOperator
op = AbarbanelGottliebPMLTEMaxwellOperator(epsilon, mu, flux_type=1,
current=Current(),
pec_tag=TAG_ALL,
absorb_tag=TAG_NONE,
add_decay=True
)
fields = op.assemble_ehpq(discr=discr)
stepper = RK4TimeStepper()
if rcon.is_head_rank:
print "order %d" % order
print "#elements=", len(mesh.elements)
# 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"])
from hedge.log import LpNorm
class FieldIdxGetter:
def __init__(self, whole_getter, idx):
self.whole_getter = whole_getter
self.idx = idx
def __call__(self):
return self.whole_getter()[self.idx]
# timestep loop -------------------------------------------------------
t = 0
pml_coeff = op.coefficients_from_width(discr, width=pml_width)
rhs = op.bind(discr, pml_coeff)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=4/c, 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 % 10 == 0 and write_output:
e, h, p, q = op.split_ehpq(fields)
visf = vis.make_file("em-%d-%04d" % (order, step))
#pml_rhs_e, pml_rhs_h, pml_rhs_p, pml_rhs_q = \
#op.split_ehpq(rhs(t, fields))
j = Current().volume_interpolant(t, discr)
vis.add_data(visf, [
("e", discr.convert_volume(e, "numpy")),
("h", discr.convert_volume(h, "numpy")),
("p", discr.convert_volume(p, "numpy")),
("q", discr.convert_volume(q, "numpy")),
("j", discr.convert_volume(j, "numpy")),
#("pml_rhs_e", pml_rhs_e),
#("pml_rhs_h", pml_rhs_h),
#("pml_rhs_p", pml_rhs_p),
#("pml_rhs_q", pml_rhs_q),
#("max_rhs_e", max_rhs_e),
#("max_rhs_h", max_rhs_h),
#("max_rhs_p", max_rhs_p),
#("max_rhs_q", max_rhs_q),
],
time=t, step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
_, _, energies_data = logmgr.get_expr_dataset("W_el+W_mag")
energies = [value for tick_nbr, value in energies_data]
assert energies[-1] < max(energies) * 1e-2
finally:
logmgr.close()
if write_output:
vis.close()
def main(write_output=True):
from hedge.timestep.runge_kutta import LSRK4TimeStepper
from math import sqrt, pi, exp
from hedge.backends import guess_run_context
rcon = guess_run_context()
epsilon0 = 8.8541878176e-12 # C**2 / (N m**2)
mu0 = 4 * pi * 1e-7 # N/A**2.
epsilon = 1 * epsilon0
mu = 1 * mu0
c = 1 / sqrt(mu * epsilon)
pml_width = 0.5
#mesh = make_mesh(a=np.array((-1,-1,-1)), b=np.array((1,1,1)),
#mesh = make_mesh(a=np.array((-3,-3)), b=np.array((3,3)),
mesh = make_mesh(
a=np.array((-1, -1)),
b=np.array((1, 1)),
#mesh = make_mesh(a=np.array((-2,-2)), b=np.array((2,2)),
pml_width=pml_width,
max_volume=0.01)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
class Current:
def volume_interpolant(self, t, discr):
from hedge.tools import make_obj_array
result = discr.volume_zeros(kind="numpy", dtype=np.float64)
omega = 6 * c
if omega * t > 2 * pi:
return make_obj_array([result, result, result])
x = make_obj_array(discr.nodes.T)
r = np.sqrt(np.dot(x, x))
idx = r < 0.3
result[idx] = (1+np.cos(pi*r/0.3))[idx] \
*np.sin(omega*t)**3
result = discr.convert_volume(result,
kind=discr.compute_kind,
dtype=discr.default_scalar_type)
return make_obj_array([-result, result, result])
order = 3
discr = rcon.make_discretization(mesh_data,
order=order,
debug=["cuda_no_plan"])
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "em-%d" % order)
from hedge.mesh import TAG_ALL, TAG_NONE
from hedge.data import GivenFunction, TimeHarmonicGivenFunction, TimeIntervalGivenFunction
from hedge.models.em import MaxwellOperator
from hedge.models.pml import \
AbarbanelGottliebPMLMaxwellOperator, \
AbarbanelGottliebPMLTMMaxwellOperator, \
AbarbanelGottliebPMLTEMaxwellOperator
op = AbarbanelGottliebPMLTEMaxwellOperator(epsilon,
mu,
flux_type=1,
current=Current(),
pec_tag=TAG_ALL,
absorb_tag=TAG_NONE,
add_decay=True)
fields = op.assemble_ehpq(discr=discr)
stepper = LSRK4TimeStepper()
if rcon.is_head_rank:
print "order %d" % order
print "#elements=", len(mesh.elements)
# 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"])
from hedge.log import LpNorm
class FieldIdxGetter:
def __init__(self, whole_getter, idx):
self.whole_getter = whole_getter
self.idx = idx
def __call__(self):
return self.whole_getter()[self.idx]
# timestep loop -------------------------------------------------------
t = 0
pml_coeff = op.coefficients_from_width(discr, width=pml_width)
rhs = op.bind(discr, pml_coeff)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=4 / c,
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 % 10 == 0 and write_output:
e, h, p, q = op.split_ehpq(fields)
visf = vis.make_file("em-%d-%04d" % (order, step))
#pml_rhs_e, pml_rhs_h, pml_rhs_p, pml_rhs_q = \
#op.split_ehpq(rhs(t, fields))
j = Current().volume_interpolant(t, discr)
vis.add_data(
visf,
[
("e", discr.convert_volume(e, "numpy")),
("h", discr.convert_volume(h, "numpy")),
("p", discr.convert_volume(p, "numpy")),
("q", discr.convert_volume(q, "numpy")),
("j", discr.convert_volume(j, "numpy")),
#("pml_rhs_e", pml_rhs_e),
#("pml_rhs_h", pml_rhs_h),
#("pml_rhs_p", pml_rhs_p),
#("pml_rhs_q", pml_rhs_q),
#("max_rhs_e", max_rhs_e),
#("max_rhs_h", max_rhs_h),
#("max_rhs_p", max_rhs_p),
#("max_rhs_q", max_rhs_q),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
_, _, energies_data = logmgr.get_expr_dataset("W_el+W_mag")
energies = [value for tick_nbr, value in energies_data]
assert energies[-1] < max(energies) * 1e-2
finally:
logmgr.close()
if write_output:
vis.close()
def test_kv_with_no_charge():
from random import seed
seed(0)
from pyrticle.units import SIUnitsWithNaturalConstants
units = SIUnitsWithNaturalConstants()
# discretization setup ----------------------------------------------------
from hedge.mesh import make_cylinder_mesh
from hedge.backends import guess_run_context
rcon = guess_run_context([])
tube_length = 100*units.MM
mesh = make_cylinder_mesh(radius=25*units.MM, height=tube_length, periodic=True)
discr = rcon.make_discretization(mesh, order=3)
dt = discr.dt_factor(units.VACUUM_LIGHT_SPEED()) / 2
final_time = 1*units.M/units.VACUUM_LIGHT_SPEED()
nsteps = int(final_time/dt)+1
dt = final_time/nsteps
# 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)
nparticles = 10000
cloud_charge = 1e-9 * units.C
electrons_per_particle = cloud_charge/nparticles/units.EL_CHARGE
el_energy = 5.2e6 * units.EV
gamma = el_energy/units.EL_REST_ENERGY()
beta = (1-1/gamma**2)**0.5
from pyrticle.distribution import KVZIntervalBeam
beam = KVZIntervalBeam(units,
total_charge=0,
p_charge=0,
p_mass=electrons_per_particle*units.EL_MASS,
radii=2*[2.5*units.MM],
emittances=2*[5 * units.MM * units.MRAD],
z_length=5*units.MM,
z_pos=10*units.MM,
beta=beta)
state = method.make_state()
method.add_particles(state, beam.generate_particles(), nparticles)
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager
from pyrticle.log import add_beam_quantities, StateObserver
observer = StateObserver(method, None)
logmgr = LogManager(mode="w")
add_beam_quantities(logmgr, observer, axis=0, beam_axis=2)
from pyrticle.distribution import KVPredictedRadius
logmgr.add_quantity(KVPredictedRadius(dt,
beam_v=beta*units.VACUUM_LIGHT_SPEED(),
predictor=beam.get_rms_predictor(axis=0),
suffix="x_rms"))
logmgr.add_quantity(KVPredictedRadius(dt,
beam_v=beta*units.VACUUM_LIGHT_SPEED(),
predictor=beam.get_total_predictor(axis=0),
suffix="x_total"))
# timestep loop -----------------------------------------------------------
vel = method.velocities(state)
from hedge.tools import join_fields
def rhs(t, y):
return join_fields([
vel,
0*vel,
0, # drecon
])
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
t = 0
from pyrticle.cloud import TimesteppablePicState
ts_state = TimesteppablePicState(method, state)
for step in xrange(nsteps):
observer.set_fields_and_state(None, ts_state.state)
logmgr.tick()
ts_state = stepper(ts_state, t, dt, rhs)
method.upkeep(ts_state.state)
t += dt
logmgr.tick()
_, _, err_table = logmgr.get_expr_dataset("(rx_rms-rx_rms_theory)/rx_rms_theory")
rel_max_rms_error = max(err for step, err in err_table)
assert rel_max_rms_error < 0.01
