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matplotlib animation:: 1-d & 2-d wave equation
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from mpl_toolkits.mplot3d import Axes3D | |
from matplotlib.pylab import plt | |
from matplotlib import animation, cm | |
import numpy as np | |
from scipy.signal import convolve, convolve2d | |
class Wave1D: | |
K = np.array([1, -2, 1]) | |
def __init__(self): | |
self.x = np.linspace(0, 100, 500) | |
self.u_curr = np.zeros(self.x.size) | |
r = np.abs(self.x - 20) / 10 | |
self.u_curr += np.where(r < 1, (np.cos(r * np.pi) + 1) / 2, 0) | |
r = np.abs(self.x - 70) / 10 | |
self.u_curr -= np.where(r < 1, (np.cos(r * np.pi) + 1) / 2, 0) | |
self.u_prev = np.array(self.u_curr) | |
(self.fig, ax) = plt.subplots() | |
ax.set_ylim(-2, 2) | |
self.line, = plt.plot(self.x, self.u_curr) | |
def update(self, _i): | |
print(_i) | |
uxx = convolve(self.u_curr, self.K, mode="same") | |
u_next = 2 * self.u_curr - self.u_prev + 0.99 * uxx | |
u_next[0] = u_next[1] | |
u_next[-1] = u_next[-2] | |
self.u_prev = self.u_curr | |
self.u_curr = u_next | |
self.line.set_data(self.x, u_next) | |
return (self.line,) | |
def make_animation(self): | |
ani = animation.FuncAnimation(self.fig, self.update, frames=600, blit=True) | |
ani.save("wave1d.mp4", writer="ffmpeg", fps=60) | |
Wave1D().make_animation() | |
class Wave2D: | |
K = np.array([ | |
[0, 1, 0], | |
[1, -4, 1], | |
[0, 1, 0] | |
]) | |
def __init__(self): | |
self.fig = plt.figure() | |
self.ax = self.fig.gca(projection="3d") | |
self.ax.view_init(elev=50., azim=45) | |
self.ax.set_zlim3d([-1, 1]) | |
self.x, self.y = np.meshgrid( | |
np.arange(-2, 3, 0.025), | |
np.arange(-2, 3, 0.025) | |
) | |
r = np.sqrt(self.x ** 2 + (self.y * 3) ** 2) | |
self.u_curr = np.where(r < 1, (np.cos(r * np.pi) + 1) / 2, 0) | |
self.u_prev = np.array(self.u_curr) | |
self.surf = None | |
def update(self, _i): | |
print(_i) | |
uxx = convolve2d(self.u_curr, self.K, mode="same") | |
u_next = 2 * self.u_curr - self.u_prev + 0.7 * uxx | |
u_next[0, :] = u_next[1, :] | |
u_next[-1, :] = u_next[-2, :] | |
u_next[:, 0] = u_next[:, 1] | |
u_next[:, -1] = u_next[:, -2] | |
self.u_prev = self.u_curr | |
self.u_curr = u_next | |
if self.surf: | |
self.surf.remove() | |
self.surf = self.ax.plot_surface( | |
self.x, self.y, self.u_curr, cmap=cm.coolwarm, | |
vmin=-0.25, vmax=0.25, linewidth=0, antialiased=False | |
) | |
return (self.surf,) | |
def make_animation(self): | |
ani = animation.FuncAnimation(self.fig, self.update, frames=600, blit=True) | |
ani.save("wave2d.mp4", writer="ffmpeg", fps=60) | |
Wave2D().make_animation() |
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