Details
| Original language | English |
|---|---|
| Pages (from-to) | 879-903 |
| Number of pages | 25 |
| Journal | Numerical Methods for Partial Differential Equations |
| Volume | 23 |
| Issue number | 4 |
| Publication status | Published - 26 Apr 2007 |
Abstract
We study an additive Schwarz based preconditioner for the hp-version of the boundary element method with quasi-uniform triangular meshes and for hypersingular integral operators. The model problem is Laplace's equation exterior to an open surface and is generic for elliptic boundary value problems of second order in bounded and unbounded domains with closed or open boundary. The preconditioner is based on a nonoverlapping subspace decomposition into a so-called wire basket space and interior functions for each element. We prove that the condition number of the preconditioned stiffness matrix has a bound, which is independent of the mesh size h and which grows only polylogarithmically in p, the maximum polynomial degree. Numerical experiments confirm this result.
Keywords
- Additive Schwarz method, Boundary element method, Domain decomposition, Iterative substructuring method, P- and hp-versions, Preconditioner
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Numerical Methods for Partial Differential Equations, Vol. 23, No. 4, 26.04.2007, p. 879-903.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An Iterative Substructuring Method for the hp-Version of the BEM on Quasi-Uniform Triangular Meshes
AU - Heuer, Norbert
AU - Leydecker, Florian
AU - Stephan, Ernst P.
PY - 2007/4/26
Y1 - 2007/4/26
N2 - We study an additive Schwarz based preconditioner for the hp-version of the boundary element method with quasi-uniform triangular meshes and for hypersingular integral operators. The model problem is Laplace's equation exterior to an open surface and is generic for elliptic boundary value problems of second order in bounded and unbounded domains with closed or open boundary. The preconditioner is based on a nonoverlapping subspace decomposition into a so-called wire basket space and interior functions for each element. We prove that the condition number of the preconditioned stiffness matrix has a bound, which is independent of the mesh size h and which grows only polylogarithmically in p, the maximum polynomial degree. Numerical experiments confirm this result.
AB - We study an additive Schwarz based preconditioner for the hp-version of the boundary element method with quasi-uniform triangular meshes and for hypersingular integral operators. The model problem is Laplace's equation exterior to an open surface and is generic for elliptic boundary value problems of second order in bounded and unbounded domains with closed or open boundary. The preconditioner is based on a nonoverlapping subspace decomposition into a so-called wire basket space and interior functions for each element. We prove that the condition number of the preconditioned stiffness matrix has a bound, which is independent of the mesh size h and which grows only polylogarithmically in p, the maximum polynomial degree. Numerical experiments confirm this result.
KW - Additive Schwarz method
KW - Boundary element method
KW - Domain decomposition
KW - Iterative substructuring method
KW - P- and hp-versions
KW - Preconditioner
UR - http://www.scopus.com/inward/record.url?scp=34547368985&partnerID=8YFLogxK
U2 - 10.1002/num.20259
DO - 10.1002/num.20259
M3 - Article
AN - SCOPUS:34547368985
VL - 23
SP - 879
EP - 903
JO - Numerical Methods for Partial Differential Equations
JF - Numerical Methods for Partial Differential Equations
SN - 0749-159X
IS - 4
ER -