Characteristic based methods for the time-domain Maxwell equations

A Comparative Study of Characteristic-Based Algorithms for the Maxwell Equations

“…Thus, all eigenvalues and eigenvectors are invariant with respect to independent variables. The resultant split one-dimensional equations for the three-dimensional problem are completely decoupled and consist of 12 scalar Riemann equations [4,5]. In this formulation, accurate simulation of electromagnetic phenomenon is restricted to fields that can be described by rectilinear coordinates.…”

“…The essential diagonalization process is simply to construct a non-singular similarity matrix and its left-hand inverse from the eigenvectors in each spatial dimension [4,5,9]. In a Cartesian frame, the Maxwell equations for an isotropic and homogeneous medium have constant coefficients.…”

“…This artifact has been known to induce spurious wave reflections from the truncated boundary and to incur sizable numerical errors [1][2][3]. In oder to eliminate or to alleviate the wave reflection from numerical boundaries, either a compatibility condition derived from the characteristic theory [4,5], or an absorbing boundary condition [6][7][8] is frequently implemented at the farfield boundary. The characteristic based concept of compatibility is preferred over the others, because the numerical procedure also enforces the directional propagation of information for wave motion.…”

“…Therefore, the characteristic based formulation on curvilinear coordinates becomes an approximation to the Riemann problem [4,5,9].…”

A scalable HPF implementation of a finite‐volume computational electromagnetics application on a CRAY T3E parallel system

“…Computational simulations are derived from discretized approximations to the time-dependent Maxwell equations [1][2][3][4][5][6][7][8][9][10]. High numerical efficiency of CEM simulation procedures can be attained either by algorithmic improvements to solve the Maxwell equations or by using scalable parallel distributed memory computer systems.…”