1 Introduction
With the continuous advancement of computing technology, various simulation technologies have attracted increasing attention. Among them, the 3D electromagnetic FDTD (finite difference time domain) simulator is a commonly used simulation method in the field of electromagnetics. Although there are many mature commercial software that support FDTD simulation, developing a simple simulator independently can better understand its working principle and adjust it according to specific needs.
This article will guide you in using Python to write a basic 3D electromagnetic FDTD simulator, and introduce how to use PyTorch's GPU acceleration function to improve simulation speed.
2. FDTD Basics
FDTD is a numerical method that solves Maxwell's equations directly in the time domain. By discretizing space and time, the continuous Maxwell equations are transformed into a series of discrete difference equations, and then the time evolution of the electric and magnetic fields is obtained through iteration.
The main equations are as follows:
-
更新磁场： Hxn+1/2=Hxn−Δt(∂Ezn∂y−∂Eyn∂z)H_x^{n+1/2} = H_x^n - \Delta t \left( \frac{\partial E_z^n}{\partial y} - \frac{\partial E_y^n}{\partial z} \right)Hxn+1/2=Hxn−Δt(∂y∂Ezn−∂z∂Eyn) Hyn+1/2=Hyn−Δt(∂Exn∂z−∂Ezn∂x)H_y^{n+1/2} = H_y^n - \Delta t \left( \frac{\partial E_x^n}{\partial z} - \frac{\partial E_z^n}{\partial x} \right)Hyn+1/2=Hyn−Δt(∂z∂Exn−∂x∂Ezn) Hzn+1/2=Hzn−Δt(∂Eyn∂x−∂Exn∂y)H_z^{n+1/2} = H_z^n - \Delta t \left( \fra