Energy evolution of multi-symplectic methods for Maxwell equations with perfectly matched layer boundary

TL;DR

This paper investigates how multi-symplectic numerical methods affect the energy behavior of 3D Maxwell equations with PML boundaries, providing energy evolution laws for these discretizations.

Contribution

It derives energy evolution laws for multi-symplectic Yee and Runge-Kutta methods applied to Maxwell equations with PML boundaries, advancing understanding of their energy properties.

Findings

Energy evolution laws are established for the discretized Maxwell equations.

The study enhances understanding of energy behavior in multi-symplectic discretizations.

Results inform the development of energy-preserving numerical schemes.

Abstract

In this paper, we consider the energy evolution of multi-symplectic methods for three-dimensional (3D) Maxwell equations with perfectly matched layer boundary, and present the energy evolution laws of Maxwell equations under the discretization of multi-symplectic Yee method and general multi-symplectic Runge-Kutta methods.