Development of a Self-Consistent Truly Multiphysics Algorithm Based Upon the Courant-Insensitive Space–Time Conservation-Element Solution-Element Method

Abstract

This paper reports on the theoretical aspects and current development status of a self-consistent truly multiphysics algorithm. The algorithm is based upon the Courant-insensitive space-time conservation-element solution-element methodology. Previous attempts for electromagnetic solutions have applicability only in constant material domains with PEC boundary conditions. This paper reports on the extension of this algorithm for the solution of the generalized Maxwell equations, including linear-dispersive materials. The numerical solution is shown to be extremely accurate on highly nonuniform meshes and reduces to the classical Yee FDTD error properties in the uniform Cartesian grid limit. Validation problems and comparison with the ubiquitous baseline FDTD algorithm will be presented in 1-D (2-D space-time). Results show that the second-order CESE method has an accuracy equivalent to fourth-sixth order FDTD for equal grids with highly discontinuous coefficients (e.g., permittivity).