"""
Solving Laplace's equation in 2d
================================

This example shows how to solve a 2d Laplace equation with spatially varying
boundary conditions.
"""

import numpy as np

from pde import CartesianGrid, solve_laplace_equation

grid = CartesianGrid([[0, 2 * np.pi], [0, 2 * np.pi]], 64)
bcs = {"x": {"value": "sin(y)"}, "y": {"value": "sin(x)"}}

res = solve_laplace_equation(grid, bcs)
res.plot()