Tangent field

import importlib
import time

import matplotlib.pyplot as plt

import nannos as nn
from nannos.formulations.tangent import get_tangent_field

We will generate a field tangent to the material interface

nh = 1500
lattice = nn.Lattice(([1, 0], [0, 1]), discretization=2**9)

x, y = lattice.grid
circ = lattice.circle((0.3, 0.3), 0.25)
rect = lattice.rectangle((0.7, 0.7), (0.2, 0.5))
grid = lattice.ones() * (3 + 0.01j)
grid[circ] = 1
grid[rect] = 1

st = lattice.Layer("pat", thickness=1, epsilon=grid)
lays = [lattice.Layer("sup"), st, lattice.Layer("sub")]
pw = nn.PlaneWave(wavelength=1 / 1.2)
sim = nn.Simulation(lays, pw, nh)

dsp = 6

FFT version

t0 = -time.time()
t = get_tangent_field(grid, sim.harmonics, normalize=False, type="fft")
t0 += time.time()
print(f"Elapsed time {t0:.4f}s")


plt.figure()
st.plot()
plt.quiver(
    x[::dsp, ::dsp],
    y[::dsp, ::dsp],
    t[0][::dsp, ::dsp],
    t[1][::dsp, ::dsp],
    scale=20,
)
plt.axis("scaled")
_ = plt.axis("off")
plt.show()

Elapsed time 1.0557s

Optimized version

t0 = -time.time()
topt = get_tangent_field(grid, sim.harmonics, normalize=False, type="opt", maxiter=1)
t0 += time.time()
print(f"Elapsed time {t0:.4f}s")

plt.figure()
st.plot()
plt.quiver(
    x[::dsp, ::dsp],
    y[::dsp, ::dsp],
    topt[0][::dsp, ::dsp],
    topt[1][::dsp, ::dsp],
    scale=20,
)
plt.axis("scaled")
_ = plt.axis("off")
plt.show()

Elapsed time 1.3593s

Optimized version (normalized)

t0 = -time.time()
topt = get_tangent_field(grid, sim.harmonics, normalize=True, type="opt", maxiter=1)
t0 += time.time()
print(f"Elapsed time {t0:.4f}s")

plt.figure()
st.plot()
plt.quiver(
    x[::dsp, ::dsp],
    y[::dsp, ::dsp],
    topt[0][::dsp, ::dsp],
    topt[1][::dsp, ::dsp],
    scale=20,
)
plt.axis("scaled")
_ = plt.axis("off")
plt.show()

Elapsed time 1.3417s

Estimated memory usage: 1126 MB