A High-Precision Integration Scheme for the Spectral-Element Time-Domain Method in Electromagnetic Simulation

A high-precision integration (HPI) scheme combined with the spectral-element time-domain (SETD) method is presented to solve the time-dependent Maxwell's equations. Spatial discretization by spectral elements will lead to block diagonal mass matrices, thus greatly alleviating the computational burden of inverting the mass matrices. A high-precision time integration method based on the matrix exponential is then employed to solve the discretized SETD system. Numerical examples demonstrate that this algorithm is unconditionally stable and very accurate.