Paper Info
Title
Stable numerical coupling of exterior and interior problems for the wave equation
Abstract
The acoustic wave equation on the whole three-dimensional space is considered with initial data and inhomogeneity having support in a bounded domain, which need not be convex. We propose and study a numerical method that approximates the solution using computations only in the interior domain and on its boundary. The transmission conditions between the interior and exterior domain are imposed by a time-dependent boundary integral equation coupled to the wave equation in the interior domain. We give a full discretization by finite elements and leapfrog time-stepping in the interior, and by boundary elements and convolution quadrature on the boundary. The direct coupling becomes stable on adding a stabilization term on the boundary. The derivation of stability estimates is based on a strong positivity property of the Calderón boundary operators for the Helmholtz and wave equations and uses energy estimates both in time and frequency domain. The stability estimates together with bounds of the consistency error yield optimal-order error bounds of the full discretization.
Year
DOI
Venue
2015
10.1007/s00211-014-0650-0
Numerische Mathematik
Keywords
Field
DocType
computational mathematics,applied mathematics
Boundary value problem,Discretization,Mathematical optimization,Mathematical analysis,Acoustic wave equation,Fictitious domain method,Free boundary problem,Poincaré–Steklov operator,Wave equation,Mathematics,Mixed boundary condition
Journal
Volume
Issue
ISSN
129
4
0945-3245
Citations 
PageRank 
References 
6
0.70
8
Authors
3
Name
Order
Citations
PageRank
Lehel Banjai1568.52
Christian Lubich2739109.24
Francisco‐Javier Sayas327437.78