A Non-Spurious Vector Spectral Element Method for Maxwell's Equations

In this paper, a non-spurious vector spectral element method is proposed to solve Maxwell's equations using E and H as variables.The mixed-order curl-conforming basis functions are used for both variables to facilitate applying boundary and interface conditions; and the interpolation degree of basis functions for E is set different from that for H to suppress the spurious modes.The proposed method can be utilized in both time domain and frequency domain, and it is very suitable for the future implementation of discontinuous Galerkin spectral element method.Numerical results demonstrate the property of spurious-free and the spectral accuracy of this method.The method has also been implemented for the more general finite element method in time and frequency domains.