TY - JOUR
T1 - On $L^2$-Stability Analysis of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions
AU - Wang , Bo
AU - Wang , Li-Lian
JO - Journal of Mathematical Study
VL - 1
SP - 65
EP - 84
PY - 2014
DA - 2014/03
SN - 47
DO - http://doi.org/10.4208/jms.v47n1.14.04
UR - https://global-sci.org/intro/article_detail/jms/9950.html
KW - Wave equation, time-domain scattering problems, exact nonreflecting boundary conditions, stability analysis, a priori estimates.
AB - <p style="text-align: justify;">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.</p>