On $L^2$-Stability Analysis of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions

On $L^2$-Stability Analysis of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions

Year:    2014

Author:    Bo Wang, Li-Lian Wang

Journal of Mathematical Study, Vol. 47 (2014), Iss. 1 : pp. 65–84

Abstract

This paper is devoted to stability analysis of the acoustic wave equation exterior to a bounded scatterer, where the unbounded computational domain is truncated by the exact time-domain circular/spherical nonreflecting boundary condition (NRBC). Different from the usual energy method, we adopt an argument that leads to $L^2$-a priori estimates with minimum regularity requirement for the initial data and source term. This needs some delicate analysis of the involved NRBC. These results play an essential role in the error analysis of the interior solvers (e.g., finite-element/spectral- element/spectral methods) for the reduced scattering problems. We also apply the technique to analyze a time-domain waveguide problem.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v47n1.14.04

Journal of Mathematical Study, Vol. 47 (2014), Iss. 1 : pp. 65–84

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Wave equation time-domain scattering problems exact nonreflecting boundary conditions stability analysis a priori estimates.

Author Details

Bo Wang

Li-Lian Wang

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