A Nodal Hybrid Continuous-Discontinuous Galerkin Time Domain Method for Maxwell’s Curl Equations

Abstract

A new nodal hybrid continuous-discontinuous Galerkin time-domain (CDGTD) method for the solution of Maxwell's curl equations is proposed and analyzed. This hy- bridization is made by clustering small collections of elements with a continuous Galerkin (CG) formalism. These cluste rs exchange information with their exterior through a discontinuous Galerkin (DG) numerical flux. This scheme shows reduced numerical dis- persion error with respect to classical DG formul ations for certain orders and numbers of clustered e lements. The spectral radius of the clustered semi-discretized operator is smaller than its DG counterpart allowing for larger time steps in e xplicit time integra- tors. Additionally, the continuity across the element boundaries allows us a reduction of the number of degrees of freedom of up to about 80% for a low-order three-dimensi onal implementation.