Constraint-Preserving Scheme for Maxwell's Equations

TL;DR

This paper introduces a constraint-preserving discretization scheme for Maxwell's equations using DVDM, demonstrating improved numerical stability and accuracy over traditional methods like Crank-Nicolson.

Contribution

The paper develops a novel DVDM-based discretization that preserves constraints at the discrete level, ensuring stability and accuracy in numerical solutions of Maxwell's equations.

Findings

DVDM discretization outperforms Crank-Nicolson in simulations

Constraint preservation is crucial for numerical stability

Discretized evolution equations confirm constraint satisfaction

Abstract

We derive the discretized Maxwell's equations using the discrete variational derivative method (DVDM), calculate the evolution equation of the constraint, and confirm that the equation is satisfied at the discrete level. Numerical simulations showed that the results obtained by the DVDM are superior to those obtained by the Crank-Nicolson scheme. In addition, we study the two types of the discretized Maxwell's equations by the DVDM and conclude that if the evolution equation of the constraint is not conserved at the discrete level, then the numerical results are also unstable.