def calculate_cavity_fields(solution, points, cavity_indexers, domains):
"""
Return the value of a cavity's field, calculated from the trace data.
"""
# cavities
E_pot_cavities = []
H_pot_cavities = []
# print(cavity_indexers)
for i in range(solution.system.N-1):
cavity_points = points[:, cavity_indexers[i]] # [:, :, 0]
H_pot_cavities.append(
maxwell_potential.magnetic_field(
domains[2*i], cavity_points, solution.system.wave_numbers[i+2]
)
)
E_pot_cavities.append(
maxwell_potential.electric_field(
domains[2*i+1], cavity_points, solution.system.wave_numbers[i+2]
)
)
# fields
## cavities
cavity_fields = [
H_pot_cavities[i] * solution.traces[2*i] \
+ E_pot_cavities[i] * \
(solution.system.mu_numbers[2+i]/solution.system.wave_numbers[2+i] * \
solution.traces[2*i+1])
for i, _ in enumerate(solution.system.cavity_grid.cavities)
]
return cavity_fields
def test_maxwell_magnetic_field_potential_rwg(default_parameters, helpers,
device_interface, precision):
"""Test Maxwell magnetic potential."""
from bempp.api import function_space
from bempp.api import GridFunction
from bempp.api.operators.potential.maxwell import magnetic_field
grid = helpers.load_grid("sphere")
space = function_space(grid, "RWG", 0)
data = helpers.load_npz_data("maxwell_magnetic_field_potential")
coefficients = data["vec"]
points = data["points"]
expected = data["result"]
fun = GridFunction(space, coefficients=coefficients)
actual = magnetic_field(
space,
points,
WAVENUMBER,
parameters=default_parameters,
precision=precision,
device_interface=device_interface,
).evaluate(fun)
_np.testing.assert_allclose(actual,
expected,
rtol=helpers.default_tolerance(precision))
def calculate_scattered_field(points, exterior_indexer, domains, solution):
"""
Return the value of the scattered field, calculated from the trace data.
"""
exterior_points = points[:, exterior_indexer] # [:, :, 0]
H_pot_ext = maxwell_potential.magnetic_field(
domains[-2], exterior_points, solution.system.wave_numbers[0]
)
E_pot_ext = maxwell_potential.magnetic_field(
domains[-1], exterior_points, solution.system.wave_numbers[0]
)
scattered_field = - H_pot_ext * solution.traces[-2] \
- E_pot_ext * (
solution.system.mu_numbers[0]/solution.system.wave_numbers[0] * solution.traces[-1]
)
return scattered_field
def calculate_cavity_fields_weak(solution, points, cavity_indexers, domains, traces):
"""
Return the value of a cavity field, calculated from the trace data.
"""
E_pot_cavities = []
H_pot_cavities = []
# print(cavity_indexers)
for i in range(solution.system.N-1):
cavity_points = points[:, cavity_indexers[i]] # [:, :, 0]
H_pot_cavities.append(
maxwell_potential.magnetic_field(
domains[i], cavity_points, solution.system.wave_numbers[i+2]
)
)
E_pot_cavities.append(
maxwell_potential.electric_field(
domains[i], cavity_points, solution.system.wave_numbers[i+2]
)
)
## cavities
cavity_fields = [
H_pot_cavities[i] * trace.dirichlet \
+ E_pot_cavities[i] * \
(solution.system.mu_numbers[2+i]/solution.system.wave_numbers[2+i] * \
trace.neumann)
for i, trace in enumerate(traces)
]
return cavity_fields
def calculate_wall_field(solution, points, wall_indexer, domains, wall_dTrace, wall_nTrace):
"""
Return the value of the field in the wall, calculated from the trace data.
"""
# wall
wall_points = points[:, wall_indexer]
H_pot_wall = maxwell_potential.magnetic_field(
domains[-2], wall_points, solution.system.wave_numbers[1])
E_pot_wall = maxwell_potential.electric_field(
domains[-1], wall_points, solution.system.wave_numbers[1])
H_pot_cavities = []
E_pot_cavities = []
# Influence of cavity
for i in range(solution.system.N-1):
H_pot_cavities.append(
maxwell_potential.magnetic_field(
domains[2*i], wall_points, solution.system.wave_numbers[1])
)
E_pot_cavities.append(
maxwell_potential.electric_field(
domains[2*i+1], wall_points, solution.system.wave_numbers[1])
)
cavity_contribution = sum([
H_pot_cavities[i] * solution.traces[2*i] \
+ E_pot_cavities[i] * (
solution.system.mu_numbers[2+i]/solution.system.wave_numbers[2+i] \
* solution.traces[2*i+1]
)
for i in range(solution.system.N-1)
])
wall_field = H_pot_wall * wall_dTrace + E_pot_wall * (solution.system.mu_numbers[1]/solution.system.wave_numbers[1] \
* wall_nTrace) - cavity_contribution
return wall_field
def calculate_wall_field_weak(solution, points, wall_indexer, domains, trace_wall, trace_cavities):
"""
Return the value of the field within the wall, calculated from the trace data.
"""
# wall
wall_points = points[:, wall_indexer]
kw = solution.system.wave_numbers[-1]
mw = solution.system.wave_numbers[-1]
H_pot_w = maxwell_potential.magnetic_field(domains[-1], wall_points, kw)
E_pot_w = maxwell_potential.electric_field(domains[-1], wall_points, kw)
H_pot_c = []
E_pot_c = []
kc_list = []
mu_list = []
for i in range(solution.system.N-1):
kc = solution.system.wave_numbers[i+2]
kc_list.append(kc)
mu_list.append(solution.system.mu_numbers[i+2])
H_pot_c.append(
maxwell_potential.magnetic_field(
domains[i], wall_points, kc
)
)
E_pot_c.append(
maxwell_potential.electric_field(
domains[i], wall_points, kc
)
)
wall_field = H_pot_w * trace_wall.dirichlet + E_pot_w * (mw/kw * trace_wall.neumann) \
+ sum([
H_pot_c[i] * trace_cavities[i].dirichlet \
+ E_pot_c[i] * (mu_list[i]/kc_list[i] * trace_cavities[i].neumann)
])
return wall_field
def calculate_scattered_field_weak(solution, points, exterior_indexer, domains, trace_wall):
"""
Return the value of the scattered field, calculated from the trace data.
"""
exterior_points = points[:, exterior_indexer]
H_pot = maxwell_potential.magnetic_field(
domains[-1], exterior_points, solution.system.wave_numbers[0]
)
E_pot = maxwell_potential.electric_field(
domains[-1], exterior_points, solution.system.wave_numbers[0]
)
k = solution.system.wave_numbers[0]
mu = solution.system.mu_numbers[0]
scattered_field = - H_pot * trace_wall.dirichlet - E_pot * (mu/k * trace_wall.neumann)
return scattered_field