From 3250edd01841acfc27d1a6cef099a7109f1795d7 Mon Sep 17 00:00:00 2001
From: Simon Collignon <scllgnn@gmail.com>
Date: Tue, 20 Apr 2021 13:20:11 +0200
Subject: [PATCH] using the hermitian symmetry of the spectrum with rfft
---
__pycache__/main.cpython-39.pyc | Bin 0 -> 1903 bytes
main.py | 36 +++++++++++++++++++-------------
2 files changed, 21 insertions(+), 15 deletions(-)
create mode 100644 __pycache__/main.cpython-39.pyc
diff --git a/__pycache__/main.cpython-39.pyc b/__pycache__/main.cpython-39.pyc
new file mode 100644
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diff --git a/main.py b/main.py
index 659d363..8681d78 100644
--- a/main.py
+++ b/main.py
@@ -11,10 +11,8 @@ xy, dx = linspace(0, 1, nn, retstep=True)
c = 2 * random.rand(nn, nn) - 1
-def cahn_hilliard_fdiff(it):
- """Cahn-Hilliard integration for it iterations using finite differences mehtod."""
-
- global c
+def cahn_hilliard_fdiff(it, c):
+ """Cahn-Hilliard integration for it iterations using finite differences method."""
cp = zeros((nn + 2, nn + 2))
f = zeros((nn + 2, nn + 2))
@@ -31,32 +29,40 @@ def cahn_hilliard_fdiff(it):
cp[1:-1, 1:-1] = cp[1:-1, 1:-1] + (dt / dx**2) * (f[0:-2, 1:-1] + f[2:, 1:-1] + f[1:-1, 0:-2] + f[1:-1, 2:] - 4 * f[1:-1, 1:-1])
c = cp[1:-1, 1:-1]
-
-def cahn_hilliard_spectral(it):
- """Cahn-Hilliard integration for it iterations using fft spectral mehtod."""
+ return c
+
- global c
+def cahn_hilliard_spectral(it, c):
+ """Cahn-Hilliard integration for it iterations using fft spectral method."""
# wavenumbers
- k = power(2 * pi * fft.fftfreq(nn, d=dx), 2)
- kk = array([k,]*nn) + array([k,]*nn).transpose()
+ kr = power(2 * pi * fft.rfftfreq(nn, d=dx), 2)
+ kc = power(2 * pi * fft.fftfreq(nn, d=dx), 2)
+ kk = array([kr,]*nn) + array([kc,]*int((nn/2)+1)) .transpose()
for _ in range(it):
- c = c + dt * fft.ifft2(-kk * fft.fft2( c**3 - c - a**2 * fft.ifft2(-kk * fft.fft2(c)).real)).real
+ c = c + dt * fft.irfft2(-kk * fft.rfft2( c**3 - c - a**2 * fft.irfft2(-kk * fft.rfft2(c)).real)).real
+
+ return c
if __name__ == "__main__":
tic = time.time()
- # cahn_hilliard_fdiff(it)
- cahn_hilliard_spectral(it)
+ c1 = cahn_hilliard_fdiff(it, c)
+ c2 = cahn_hilliard_spectral(it, c)
toc = time.time() - tic
print(f"Elapsed time is {toc} seconds.")
-
- plt.contourf(xy, xy, c, cmap="jet")
+
+ fig, (ax1, ax2) = plt.subplots(1, 2)
+ fig.suptitle(f"Cahn-Hilliard integration for {it} iterations ")
+ ax1.contourf(xy, xy, c1, cmap="jet")
+ ax1.set_title("Finite differences method")
+ ax2.contourf(xy, xy, c2 , cmap="jet")
+ ax2.set_title("Spectral method")
plt.show()
--
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