Computation of far-field solutions based on exact nonreflecting boundary conditions for the time-dependent wave equation

✍ Scribed by Lonny L. Thompson; Runnong Huan

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 868 KB
• Volume: 190
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(00)00178-x

✦ Synopsis

In this work we show how to combine in the exact nonre¯ecting boundary conditions (NRBC) ®rst derived by Grote and Keller, the calculation of the exterior (far-®eld) solution for time-dependent radiation and scattering in an unbounded domain. At each discrete time step, radial modes computed on a spherical arti®cial boundary which drive the exact NRBC for the near-®eld solution, are imposed as Cauchy data for the radial wave equation in the far-®eld. Similar to the far-®eld computation scheme used by Wright, the radial modes in the exterior region are computed using an explicit ®nite dierence solver. However, instead of using an `in®nite grid', we truncate the exterior radial grid at the far-®eld point of interest, and for each harmonic, impose the same exact NRBC used for the near-®eld truncation boundary, here expressed in modal form. Using this approach, two dierent methods for extrapolating the near-®eld solution to the far-®eld are possible. In the ®rst, the near-®eld solution is computed using the exact NRBC, then, based on the solution for the radial modes evaluated on the arti®cial boundary, the exterior solution may be computed as a post-process. In the second, we show how to compute the far-®eld solution concurrently with the near-®eld solution and the NRBC. Numerical studies demonstrate that the method is highly accurate and ef®cient for direct time-domain computations of far-®eld solutions.