On $L^2$-Stability Analysis of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions (Journal of Mathematical Study, 2014)
This paper is devoted to stability analysis of the acoustic wave equationexterior 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 leadsto $L^2$-a priori estimates with minimum regularity requirement for the initial data andsource term. This needs some delicate analysis of the involved NRBC. These resultsplay 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 thetechnique to analyze a time-domain waveguide problem.