a1 Department of Mathematics and Statistics, The University of New Mexico, Albuquerque, NM 87131, USA E-mail: email@example.com
We consider the efficient evaluation of accurate radiation boundary conditions for time domain simulations of wave propagation on unbounded spatial domains. This issue has long been a primary stumbling block for the reliable solution of this important class of problems. In recent years, a number of new approaches have been introduced which have radically changed the situation. These include methods for the fast evaluation of the exact nonlocal operators in special geometries, novel sponge layers with reflectionless interfaces, and improved techniques for applying sequences of approximate conditions to higher order. For the primary isotropic, constant coefficient equations of wave theory, these new developments provide an essentially complete solution of the numerical radiation condition problem.
* Supported, in part, by NSF Grant DMS-9600146, the Institute for Computational Mechanics in Propulsion (ICOMP), NASA, Lewis Research Center, Cleveland, Ohio; DARPA/AFOSR Contract F49620-95-C-0075; and, while in residence at the Courant Institute, DOE Contract DEFGO288ER25053.