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A least squares coupling method with finite elements and boundary elements for transmission problems
- Source :
- Computers & Mathematics with Applications. 48(7-8):995-1016
- Publication Year :
- 2004
- Publisher :
- Elsevier BV, 2004.
-
Abstract
- We analyze a least squares formulation for the numerical solution of second-order lineartransmission problems in two and three dimensions, which allow jumps on the interface. In a bounded domain the second-order partial differential equation is rewritten as a first-order system; the part of the transmission problem which corresponds to the unbounded exterior domain is reformulated by means of boundary integral equations on the interface. The least squares functional is given in terms of Sobolev norms of order -1 and of order 1/2. These norms are computed by approximating the corresponding inner products using multilevel preconditioners for a second-order elliptic problem in a bounded domain @? and for the weakly singular integral operator of the single layer potential on its boundary @[email protected]?. As preconditioners we use both multigrid and BPX algorithms, and the preconditioned system has bounded or mildly growing condition number. Numerical experiments confirm our theoretical results.
- Subjects :
- Partial differential equation
Mathematical analysis
Finite elements
Boundary (topology)
Singular integral
Boundary elements
Least squares
Least squares methods
Domain (mathematical analysis)
Sobolev space
Multilevel preconditioners
Computational Mathematics
Multigrid method
Computational Theory and Mathematics
Modeling and Simulation
Bounded function
Modelling and Simulation
Transmission problems
Mathematics
Subjects
Details
- ISSN :
- 08981221
- Volume :
- 48
- Issue :
- 7-8
- Database :
- OpenAIRE
- Journal :
- Computers & Mathematics with Applications
- Accession number :
- edsair.doi.dedup.....746def9f9eb979a49950548e56a35988
- Full Text :
- https://doi.org/10.1016/j.camwa.2004.10.002