A Class of Explicit Divergence-Free Methods for Maxwell’s Equations With Dirichlet Boundary Conditions

Abstract

In this paper, we focus on the numerical solutions of Maxwell’s equations with Dirichlet boundary conditions in rectangular coordinate. A class of explicit methods is derived by using an effective solver for a system of ordinary differential equations which is obtained by approximating on spatial fields. A significant advantage of this class of methods is their simplicity and their ease of implementation. The error estimates presented in this paper show that the numerical solutions obtained by this class of methods is of high-order. The main advantage of this class of methods is that it is divergence-free.

Keywords

• Computation theory
• Dirichlet boundary value problem
• divergence-free methods
• electromagnetic propagation
• Maxwell’s equations
• time-domain methods