Volume 47, Issue 1
On L2-Stability Analysis of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions

Bo Wang & Li-Lian Wang

J. Math. Study, 47 (2014), pp. 65-84.

Published online: 2014-03

Preview Full PDF 468 1577
Export citation
  • Abstract

This paper is devoted to stability analysis of the acoustic wave equation exterior to a bounded scatterer, where the unbounded computational domain is trun- cated by the exact time-domain circular/spherical nonreflecting boundary condition (NRBC). Different from the usual energy method, we adopt an argument that leads to L2 -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.

  • Keywords

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

  • AMS Subject Headings

65R10 65N35 65E05 65M70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

bowanghn@gmail.com (Bo Wang)

LiLian@ntu.edu.sg (Li-Lian Wang)

  • BibTex
  • RIS
  • TXT
@Article{JMS-47-65, author = {Wang , Bo and Wang , Li-Lian }, title = {On L2-Stability Analysis of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions}, journal = {Journal of Mathematical Study}, year = {2014}, volume = {47}, number = {1}, pages = {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 trun- cated by the exact time-domain circular/spherical nonreflecting boundary condition (NRBC). Different from the usual energy method, we adopt an argument that leads to L2 -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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v47n1.14.04}, url = {http://global-sci.org/intro/article_detail/jms/9950.html} }
TY - JOUR T1 - On L2-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://dor.org/10.4208/jms.v47n1.14.04 UR - https://global-sci.org/intro/article_detail/jms/9950.html KW - Wave equation KW - time-domain scattering problems KW - exact nonreflecting boundary conditions KW - stability analysis KW - a priori estimates AB -

This paper is devoted to stability analysis of the acoustic wave equation exterior to a bounded scatterer, where the unbounded computational domain is trun- cated by the exact time-domain circular/spherical nonreflecting boundary condition (NRBC). Different from the usual energy method, we adopt an argument that leads to L2 -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.

Bo Wang & Li-Lian Wang. (2014). On L2-Stability Analysis of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions. Journal of Mathematical Study. 47 (1). 65-84. doi:10.4208/jms.v47n1.14.04
Copy to clipboard
The citation has been copied to your clipboard