In this talk, we devise a new Runge-Kutta Discontinuous Galerkin (RKDG) method that achieves full high-order convergence in time and space while keeping the timestep proportional to the spatial mesh-size. To this end, we derive an extension to non-autonomous linear systems of the mth-order, m-stage strong stability preserving Runge-Kutta (SSP-RK) scheme with low storage described in Gottlieb et...

The integration of complicated oscillatory functions arises in computational electromagnetics when evaluating signals produced by the propagation of electromagnetic radiation through the anisotropic layers of a geological formation. The computation of exact integrals involves the evaluation of Sommerfeld integrals. The matrix pencil method is used for the numerical approximation of such signals...

While a number of increasingly sophisticated numerical methods have been developed for time-dependent problems in electromagnetics, the Yee scheme is still widely used in the applied fields, mainly due to its simplicity and computational efficiency. A fundamental drawback of the method is the use of staircase boundary approximations, giving inconsistent results. Usually experience of numerical ...

Laplace’s differential equation is one of the most important equations which describe continuity a system in various fields engineering. As gets more complex, need for solving this numerically rises. In paper we present an accuracy investigation three significant numerical methods used computational electromagnetics by applying them to solve two-dimensional domain with Dirichlet boundary condit...

This paper is concerned with the fast iterative solution of linear systems arising from finite difference discretizations in electromagnetics. The sweeping preconditioner with moving perfectly matched layers previously developed for the Helmholtz equation is adapted for the popular Yee grid scheme for wave propagation in inhomogeneous, anisotropic media. Preliminary numerical results are presen...

A type of bell-shaped compact high order window function ψ(x, y) is studied, and closed analytic and approximation formulas are derived for its Hankel transforms. Applications of these results are presented as fast algorithms for calculating dyadic Green’s functions for electromagnetic scattering in multilayered media. Numerical results in electromagnetics are provided to demonstrate the accura...

This paper is concerned with the derivation of a priori and a posteriori error bounds for a class of linear functionals arising in electromagnetics which represent the far-field pattern of the scattered electromagnetic field. The a posteriori error bound is implemented into an adaptive finite element algorithm, and a series of numerical experiments is presented.

The objective of this work is to present a novel, robust, high-order accurate Immersed Interface/Boundary Method (IIM ). In contrast to other immersed methods, which lack a posteriori check of the numerical stability, the method presented herein combines a local Taylor-series expansion at irregular grid points with a local stability condition as part of the design process. Furthermore, this wor...

We consider preconditioning strategies for the iterative solution of dense complex symmetric nonHermitian systems arising in computational electromagnetics. We consider in particular sparse approximate inverse preconditioners that use a static nonzero pattern selection. The novelty of our approach comes from using a di erent nonzero pattern selection for the original matrix from that for the pr...