louity

import matplotlib.pyplot as plt 
import torch

def laplacian_per(f, dx, dy):
    f_per = torch.cat([f[...,[-1]], f, f[...,[0]]], dim=-1)
    f_per = torch.cat([f_per[...,[-1],:], f_per, f_per[...,[0],:]], dim=-2)
    return ((f_per[...,2:,1:-1] + f_per[...,:-2,1:-1] - 2*f_per[...,1:-1,1:-1]) / dx**2 \
           + (f_per[...,1:-1,2:] + f_per[...,1:-1,:-2]- 2*f_per[...,1:-1,1:-1]) / dy**2)

xmin = 0.0