Bounded Error Schemes for the Wave Equation on Complex Domains

This paper considers the application of the method of boundary penalty terms ("SAT") to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell's equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g. the staggered Yee scheme) - we achieve a decrease of two orders of magnitude in the level of the L2-error

Research in Applied Mathematics, Fluid Mechanics and Computer Science

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1998 through March 31, 1999

Numerical evaluation of a non-conforming discontinuous Galerkin method on triangular meshes for solving the time-domain Maxwell equations

We report on a detailed numerical evaluation of the non-dissipative, non-conforming discontinuous Galerkin (DG) method on triangular meshes, for solving the two-dimensional time-domain Maxwell equations. This DG method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements of the mesh, with a second order leap-frog time integration scheme. Moreover, non-conforming meshes with arbitrary-level hanging nodes are allowed. Here, our objective is to assess the convergence, the stability and the efficiency of the method, but also discuss its limitations, through numerical experiments for 2D propagation problems in homogeneous and heterogeneous media with various types and locations of material interfaces

NASA Langley Scientific and Technical Information Output: 1998

This document is a compilation of the scientific and technical information that the Langley Research Center has produced during the calendar year 1998. Included are citations for Technical Publications, Conference Publications, Technical Memorandums, Contractor Reports, Journal Articles and Book Publications, Meeting Presentations, Technical Talks, and Patents