LRBF-Based energy-conserving time splitting schemes for the 2D Maxwell equations

Abstract

In this paper, several energy-conserving numerical schemes are constructed for solving the two-dimensional Maxwell equations. Initially, the original problem is decomposed into two one-dimensional subproblems using operator splitting techniques. Subsequently, for spatial discretization, we employ the local radial basis function (LRBF) method, while for temporal discretization, three different splitting composition methods are selected, including the Lie-Trotter method, the Strang method, and the three-stage fourth-order splitting method. Through an analysis of the structural characteristics of the spatial differential matrices generated by the LRBF method, the unconditional stability and energy conservation properties of the fully discretized schemes are further proved. Numerical experiments validate the temporal convergence accuracy of the three numerical schemes and the preservation of their relevant properties.