source = [mp.EigenModeSource(src,
eig_band = 1,
direction=mp.NO_DIRECTION,
eig_kpoint=kpoint,
size = source_size,
center=source_center)]
#----------------------------------------------------------------------
#- geometric objects
#----------------------------------------------------------------------
Nx = 10
Ny = 10
design_region = mp.Volume(center=mp.Vector3(), size=mp.Vector3(1, 1, 0))
rho_vector = 11*np.random.rand(Nx*Ny) + 1
basis = mpa.BilinearInterpolationBasis(volume=design_region,Nx=Nx,Ny=Ny,rho_vector=rho_vector)
geometry = [
mp.Block(center=mp.Vector3(x=-Sx/4), material=mp.Medium(index=3.45), size=mp.Vector3(Sx/2, 0.5, 0)), # horizontal waveguide
mp.Block(center=mp.Vector3(y=Sy/4), material=mp.Medium(index=3.45), size=mp.Vector3(0.5, Sy/2, 0)), # vertical waveguide
mp.Block(center=design_region.center, size=design_region.size, epsilon_func=basis.func()) # design region
]
sim = mp.Simulation(cell_size=cell_size,
boundary_layers=pml_layers,
geometry=geometry,
sources=source,
eps_averaging=False,
resolution=resolution)
#----------------------------------------------------------------------
eig_band = 1,
direction=mp.NO_DIRECTION,
eig_kpoint=kpoint,
size = source_size,
center=source_center)]
#----------------------------------------------------------------------
#- geometric objects
#----------------------------------------------------------------------
geometry = [mp.Block(center=mp.Vector3(), material=mp.Medium(index=3.45), size=mp.Vector3(mp.inf, 0.5, 0) )]
Nx = 10
Ny = 10
design_size = mp.Vector3(1, 1, 0)
design_region = mpa.Subregion(name='design', center=mp.Vector3(), size=design_size)
basis = mpa.BilinearInterpolationBasis(region=design_region,Nx=Nx,Ny=Ny)
beta_vector = 11*np.random.rand(Nx*Ny) + 1
design_function = basis.parameterized_function(beta_vector)
design_object = [mp.Block(center=design_region.center, size=design_region.size, epsilon_func = design_function.func())]
geometry += design_object
sim = mp.Simulation(cell_size=cell_size,
boundary_layers=pml_layers,
geometry=geometry,
sources=sources,
eps_averaging=False,
resolution=resolution)
direction=mp.NO_DIRECTION,
eig_kpoint=kpoint,
size=source_size,
center=source_center)
]
#----------------------------------------------------------------------
#- geometric objects
#----------------------------------------------------------------------
Nx = 10
Ny = 10
design_region1 = mp.Volume(center=mp.Vector3(-.5), size=mp.Vector3(0.5, 1, 0))
rho_vector1 = 11 * np.random.rand(Nx * Ny) + 1
basis1 = mpa.BilinearInterpolationBasis(volume=design_region1,
Nx=Nx,
Ny=Ny,
rho_vector=rho_vector1)
design_region2 = mp.Volume(center=mp.Vector3(.5), size=mp.Vector3(0.5, 1, 0))
rho_vector2 = 11 * np.random.rand(Nx * Ny) + 1
basis2 = mpa.BilinearInterpolationBasis(volume=design_region2,
Nx=Nx,
Ny=Ny,
rho_vector=rho_vector2)
bases = [basis1, basis2]
geometry = [
mp.Block(center=mp.Vector3(x=-Sx / 4),
material=mp.Medium(index=3.45),
size=mp.Vector3(Sx / 2, 0.5, 0)), # horizontal waveguide
mp.Block(center=mp.Vector3(y=Sy / 4),
def run_test(self, resolution, Nx, Ny):
Sx = 1
Sy = 1
z = lambda x, y: 5 * np.abs((x**3 + y**2 + x**2 * y)) + 1
cell_size = mp.Vector3(Sx, Sy)
design_size = mp.Vector3(Sx, Sy, 0)
design_region = mpa.Subregion(name='design',
center=mp.Vector3(),
size=design_size)
basis = mpa.BilinearInterpolationBasis(region=design_region,
Nx=Nx,
Ny=Ny)
rho_x = np.linspace(-Sx / 2, Sx / 2, Nx)
rho_y = np.linspace(-Sy / 2, Sy / 2, Ny)
rho_X, rho_Y = np.meshgrid(rho_x, rho_y)
rho = z(rho_X, rho_Y)
beta_vector = rho.reshape(rho.size, order='C')
design_function = basis.parameterized_function(beta_vector)
design_object = [
mp.Block(center=design_region.center,
size=design_region.size,
epsilon_func=design_function.func())
]
geometry = design_object
sim = mp.Simulation(cell_size=cell_size,
geometry=geometry,
resolution=resolution)
sim.init_sim()
(x_interp, y_interp, z_interp,
w) = sim.get_array_metadata(center=mp.Vector3(), size=cell_size)
eps_data = sim.get_array(center=mp.Vector3(),
size=cell_size,
component=mp.Dielectric)
rho_X_interp, rho_Y_interp = np.meshgrid(x_interp, y_interp)
rho_interp_true = z(rho_X_interp, rho_Y_interp)
A = mpa.gen_interpolation_matrix(rho_x, rho_y, np.array(x_interp),
np.array(y_interp))
rho_interp_hat = A * rho.reshape(rho.size, order='C')
# Calculate errors
sim_err = np.mean(
np.abs(
eps_data.reshape(eps_data.size, order='C') -
rho_interp_true.reshape(rho_interp_true.size, order='C'))**2)
A_err = np.mean(
np.abs(rho_interp_hat -
rho_interp_true.reshape(rho_interp_true.size, order='C'))**
2)
meep_err = np.mean(
np.abs(rho_interp_hat -
eps_data.reshape(eps_data.size, order='C'))**2)
print("Simulation Mean Squared Error: ",
sim_err)
print("Interpolation Matrix Mean Squared Error: ",
A_err)
print("MSE between interp. matrix and meep's dielectric function: ",
meep_err)
'''from matplotlib import pyplot as plt
plt.figure()
plt.imshow(eps_data)
plt.title('Bilinear Interpolation')
plt.figure()
plt.imshow(rho_interp_hat.reshape(rho_interp_true.shape,order='C'))
plt.title('Sparse Matrix Solution')
plt.figure()
plt.imshow(rho_interp_true)
plt.title('Analytic Solution')
plt.show()'''
return sim_err, A_err, meep_err