Comparison of two discontinuous spectral element methods

This paper is concerned with the comparison of two spectral Discontinuous Galerkin Time-Domain (DGTD) methods for the solution of Maxwell's equations in two-dimensional space. The first scheme is based on the conventional mass-lumping technique, where the same set of points are chosen for both the interpolation base functions and the numerical integration of coefficients. The second scheme is a newly proposed approach, called the Weight-Adjusted discontinuous Galerkin (WADG) method. Several numerical examples are presented to evaluate the performance of the two methods. It is shown that although the two methods need the same storage capacity, the WADG method has higher accuracy. (authors)