Efficient energy structure-preserving schemes for three-dimensional Maxwell's equations

Abstract

Two energy structure-preserving schemes are proposed for Maxwell's equations in three dimensions. The Maxwell's equations are split into several local one-dimensional subproblems which successfully reduces the scale of algebraic equations to be solved. To improve the convergence rate in space and to keep the sparsity of the resulting algebraic equations, the spatial derivatives are approximated by high order compact method. Some key indicators, such as stability, energy structure-preserving and convergence of the schemes are investigated. To make the theoretical more persuasive, some numerical examples are shown. Numerical results are accord with the theoretical results. This provides a practical approach to construct efficient structure-preserving algorithms multidimensional Maxwell's equations.