def test_ff_error(self):
sucemfem.Utilities.Optimization.set_dolfin_optimisation(True)
### Postprocessing requests
theta_deg = N.linspace(10, 170, 161)
no_ff_pts = len(theta_deg)
phi_deg = N.zeros(no_ff_pts)
### Problem parameters
freq = 1.0e+9 # Frequency
lam = c0/freq
l = lam/4 # Dipole length
I = 1.0 # Dipole current
source_direction_z = N.array([0,0,1.]) # Source orientation
source_direction_x = N.array([1.,0,0]) # Source orientation
source_direction_y = N.array([0,1,0.]) # Source orientation
source_centre = N.array([0,0,0.]) # Position of the source
source_endpoints_z = N.array(
[-source_direction_z*l/2, source_direction_z*l/2]) + source_centre
source_endpoints_x = N.array(
[-source_direction_x*l/2, source_direction_x*l/2]) + source_centre
source_endpoints_y = N.array(
[-source_direction_y*l/2, source_direction_y*l/2]) + source_centre
### Discretisation settings
order = 2
domain_size = N.array([lam]*3)*1
max_edge_len = lam/6
mesh = get_centred_cube(domain_size, max_edge_len)
### Implementation
#
## Set up materials function with all free-space
material_mesh_func = dolfin.MeshFunction('uint', mesh, 3)
material_mesh_func.set_all(0)
materials = {0:dict(eps_r=1, mu_r=1),}
## Set up 1st-order analytical ABC
abc = ABCBoundaryCondition()
abc.set_region_number(1)
bcs = BoundaryConditions()
bcs.add_boundary_condition(abc)
## Set up high level problem class
dp = DrivenProblemABC()
dp.set_mesh(mesh)
dp.set_basis_order(order)
dp.set_material_regions(materials)
dp.set_region_meshfunction(material_mesh_func)
dp.set_boundary_conditions(bcs)
## Set up current fillament source
current_sources = sucemfem.Sources.current_source.CurrentSources()
fillament_source = FillamentCurrentSource()
fillament_source.no_integration_points = 1000
fillament_source.set_source_endpoints(source_endpoints_z)
fillament_source.set_value(I)
current_sources.add_source(fillament_source)
## Set source in problem container
dp.set_sources(current_sources)
dp.init_problem()
dp.set_frequency(freq)
## Get sytem LHS matrix and RHS Vector
A = dp.get_LHS_matrix()
b_z = dp.get_RHS()
fillament_source.set_source_endpoints(source_endpoints_x)
b_x = dp.get_RHS()
fillament_source.set_source_endpoints(source_endpoints_y)
b_y = dp.get_RHS()
#import pdb ; pdb.set_trace()
A
print 'solve using UMFPack'
umf_solver = sucemfem.Utilities.LinalgSolvers.UMFPACKSolver(A)
x_z = umf_solver.solve(b_z)
x_x = umf_solver.solve(b_x)
x_y = umf_solver.solve(b_y)
## Post-process solution to obtain far-field
print 'calculating far field'
surf_ntff = surface_ntff.NTFF(dp.function_space)
surf_ntff.set_dofs(x_z)
surf_ntff.set_frequency(freq)
surf_E_ff_z = N.array([surf_ntff.calc_pt(th_deg, ph_deg)
for th_deg, ph_deg in zip(theta_deg, phi_deg)])
surf_E_theta_z = surf_E_ff_z[:,0]
surf_E_phi_z = surf_E_ff_z[:,1]
surf_ntff.set_dofs(x_x)
surf_E_ff_x = N.array([surf_ntff.calc_pt(th_deg+90, ph_deg)
for th_deg, ph_deg in zip(theta_deg, phi_deg)])
surf_E_theta_x = surf_E_ff_x[:,0]
surf_E_phi_x = surf_E_ff_x[:,1]
surf_ntff.set_dofs(x_y)
surf_E_ff_y = N.array([surf_ntff.calc_pt(th_deg+90, ph_deg)
for th_deg, ph_deg in zip(theta_deg, phi_deg)])
surf_E_theta_y = surf_E_ff_y[:,0]
surf_E_phi_y = surf_E_ff_y[:,1]
## Calculate some errors relative to the analytical solution
an_E_theta = [current_fillament_farfield.eval_E_theta(freq, l, I, th)
for th in N.deg2rad(theta_deg)]
err_z = normalised_RMS(
surf_E_theta_z, an_E_theta, surf_E_phi_z)
err_theta_z = normalised_RMS(surf_E_theta_z, an_E_theta)
err_abs_theta_z = normalised_RMS(N.abs(surf_E_theta_z),
N.abs(an_E_theta))
err_x = normalised_RMS(
surf_E_theta_x, an_E_theta, surf_E_phi_x)
err_theta_x = normalised_RMS(surf_E_theta_x, an_E_theta)
err_abs_theta_x = normalised_RMS(N.abs(surf_E_theta_x),
N.abs(an_E_theta))
err_y = normalised_RMS(
surf_E_theta_y, an_E_theta, surf_E_phi_y)
err_theta_y = normalised_RMS(surf_E_theta_y, an_E_theta)
err_abs_theta_y = normalised_RMS(N.abs(surf_E_theta_y),
N.abs(an_E_theta))
print 'Far-field RMS error: ', err_z, err_x, err_y
# Expected error for lam/6 mesh, 2nd order discretisation,
# lam/4 current fillament source is ~4.685%
self.assertTrue(err_z < 4.7)
self.assertTrue(err_x < 4.7)
self.assertTrue(err_z < 4.7)
print 'solve using UMFPack'
umf_solver = sucemfem.Utilities.LinalgSolvers.UMFPACKSolver(A)
x = umf_solver.solve(b)
## Post-process solution to obtain far-field
print 'calculating far field'
surf_ntff = surface_ntff.NTFF(dp.function_space)
surf_ntff.set_dofs(x)
surf_ntff.set_frequency(freq)
surf_E_ff = N.array([surf_ntff.calc_pt(th_deg, ph_deg)
for th_deg, ph_deg in zip(theta_deg, phi_deg)])
surf_E_theta = surf_E_ff[:,0]
surf_E_phi = surf_E_ff[:,1]
## Calculate some errors relative to the analytical solution
an_E_theta = [current_fillament_farfield.eval_E_theta(freq, l, I, th)
for th in N.deg2rad(theta_deg)]
start=10 ; stop=-10 # Don't include the very ends
err = normalised_RMS(
surf_E_theta[start:stop], an_E_theta[start:stop], surf_E_phi[start:stop])
err_theta = normalised_RMS(surf_E_theta[start:stop], an_E_theta[start:stop])
err_abs_theta = normalised_RMS(N.abs(surf_E_theta[start:stop]),
N.abs(an_E_theta[start:stop]))
print 'Far-field RMS error: ', err
print 'plotting'
pylab.figure()
pylab.plot(theta_deg, N.abs(surf_E_theta), label='|E_theta|')
pylab.plot(theta_deg, N.abs(surf_E_phi), label='|E_phi|')
an_E_theta = [sucemfem.Testing.Analytical.current_fillament_farfield.eval_E_theta(freq, l, I, th) for th in N.deg2rad(theta_deg)]
pylab.plot(theta_deg, N.abs(an_E_theta), label='analytical')
def test_ff_error(self):
sucemfem.Utilities.Optimization.set_dolfin_optimisation(True)
### Postprocessing requests
theta_deg = N.linspace(10, 170, 161)
no_ff_pts = len(theta_deg)
phi_deg = N.zeros(no_ff_pts)
### Problem parameters
freq = 1.0e+9 # Frequency
lam = c0 / freq
l = lam / 4 # Dipole length
I = 1.0 # Dipole current
source_direction_z = N.array([0, 0, 1.]) # Source orientation
source_direction_x = N.array([1., 0, 0]) # Source orientation
source_direction_y = N.array([0, 1, 0.]) # Source orientation
source_centre = N.array([0, 0, 0.]) # Position of the source
source_endpoints_z = N.array([
-source_direction_z * l / 2, source_direction_z * l / 2
]) + source_centre
source_endpoints_x = N.array([
-source_direction_x * l / 2, source_direction_x * l / 2
]) + source_centre
source_endpoints_y = N.array([
-source_direction_y * l / 2, source_direction_y * l / 2
]) + source_centre
### Discretisation settings
order = 2
domain_size = N.array([lam] * 3) * 1
max_edge_len = lam / 6
mesh = get_centred_cube(domain_size, max_edge_len)
### Implementation
#
## Set up materials function with all free-space
material_mesh_func = dolfin.MeshFunction('uint', mesh, 3)
material_mesh_func.set_all(0)
materials = {
0: dict(eps_r=1, mu_r=1),
}
## Set up 1st-order analytical ABC
abc = ABCBoundaryCondition()
abc.set_region_number(1)
bcs = BoundaryConditions()
bcs.add_boundary_condition(abc)
## Set up high level problem class
dp = DrivenProblemABC()
dp.set_mesh(mesh)
dp.set_basis_order(order)
dp.set_material_regions(materials)
dp.set_region_meshfunction(material_mesh_func)
dp.set_boundary_conditions(bcs)
## Set up current fillament source
current_sources = sucemfem.Sources.current_source.CurrentSources()
fillament_source = FillamentCurrentSource()
fillament_source.no_integration_points = 1000
fillament_source.set_source_endpoints(source_endpoints_z)
fillament_source.set_value(I)
current_sources.add_source(fillament_source)
## Set source in problem container
dp.set_sources(current_sources)
dp.init_problem()
dp.set_frequency(freq)
## Get sytem LHS matrix and RHS Vector
A = dp.get_LHS_matrix()
b_z = dp.get_RHS()
fillament_source.set_source_endpoints(source_endpoints_x)
b_x = dp.get_RHS()
fillament_source.set_source_endpoints(source_endpoints_y)
b_y = dp.get_RHS()
#import pdb ; pdb.set_trace()
A
print 'solve using UMFPack'
umf_solver = sucemfem.Utilities.LinalgSolvers.UMFPACKSolver(A)
x_z = umf_solver.solve(b_z)
x_x = umf_solver.solve(b_x)
x_y = umf_solver.solve(b_y)
## Post-process solution to obtain far-field
print 'calculating far field'
surf_ntff = surface_ntff.NTFF(dp.function_space)
surf_ntff.set_dofs(x_z)
surf_ntff.set_frequency(freq)
surf_E_ff_z = N.array([
surf_ntff.calc_pt(th_deg, ph_deg)
for th_deg, ph_deg in zip(theta_deg, phi_deg)
])
surf_E_theta_z = surf_E_ff_z[:, 0]
surf_E_phi_z = surf_E_ff_z[:, 1]
surf_ntff.set_dofs(x_x)
surf_E_ff_x = N.array([
surf_ntff.calc_pt(th_deg + 90, ph_deg)
for th_deg, ph_deg in zip(theta_deg, phi_deg)
])
surf_E_theta_x = surf_E_ff_x[:, 0]
surf_E_phi_x = surf_E_ff_x[:, 1]
surf_ntff.set_dofs(x_y)
surf_E_ff_y = N.array([
surf_ntff.calc_pt(th_deg + 90, ph_deg)
for th_deg, ph_deg in zip(theta_deg, phi_deg)
])
surf_E_theta_y = surf_E_ff_y[:, 0]
surf_E_phi_y = surf_E_ff_y[:, 1]
## Calculate some errors relative to the analytical solution
an_E_theta = [
current_fillament_farfield.eval_E_theta(freq, l, I, th)
for th in N.deg2rad(theta_deg)
]
err_z = normalised_RMS(surf_E_theta_z, an_E_theta, surf_E_phi_z)
err_theta_z = normalised_RMS(surf_E_theta_z, an_E_theta)
err_abs_theta_z = normalised_RMS(N.abs(surf_E_theta_z),
N.abs(an_E_theta))
err_x = normalised_RMS(surf_E_theta_x, an_E_theta, surf_E_phi_x)
err_theta_x = normalised_RMS(surf_E_theta_x, an_E_theta)
err_abs_theta_x = normalised_RMS(N.abs(surf_E_theta_x),
N.abs(an_E_theta))
err_y = normalised_RMS(surf_E_theta_y, an_E_theta, surf_E_phi_y)
err_theta_y = normalised_RMS(surf_E_theta_y, an_E_theta)
err_abs_theta_y = normalised_RMS(N.abs(surf_E_theta_y),
N.abs(an_E_theta))
print 'Far-field RMS error: ', err_z, err_x, err_y
# Expected error for lam/6 mesh, 2nd order discretisation,
# lam/4 current fillament source is ~4.685%
self.assertTrue(err_z < 4.7)
self.assertTrue(err_x < 4.7)
self.assertTrue(err_z < 4.7)
umf_solver = sucemfem.Utilities.LinalgSolvers.UMFPACKSolver(A)
x_z = umf_solver.solve(b_z)
## Post-process solution to obtain far-field
print 'calculating far field'
var_ntff = variational_ntff.NTFF(dp.function_space)
var_ntff.set_dofs(x_z)
var_ntff.set_frequency(freq)
surf_E_ff_z = N.array([
var_ntff.calc_pt(th_deg, ph_deg)
for th_deg, ph_deg in zip(theta_deg, phi_deg)
])
surf_E_theta_z = surf_E_ff_z[:, 0]
surf_E_phi_z = surf_E_ff_z[:, 1]
## Calculate some errors relative to the analytical solution
an_E_theta = [
current_fillament_farfield.eval_E_theta(freq, l, I, th)
for th in N.deg2rad(theta_deg)
]
err_z = normalised_RMS(surf_E_theta_z, an_E_theta, surf_E_phi_z)
err_theta_z = normalised_RMS(surf_E_theta_z, an_E_theta)
err_abs_theta_z = normalised_RMS(N.abs(surf_E_theta_z), N.abs(an_E_theta))
print 'Far-field RMS error: ', err_z
# Expected error for lam/6 mesh, 2nd order discretisation,
# lam/4 current fillament source is ~4.685%
# self.assertTrue(err_z < 4.7)
# self.assertTrue(err_x < 4.7)
# self.assertTrue(err_z < 4.7)