Details
| Original language | English |
|---|---|
| Pages (from-to) | 211-216 |
| Number of pages | 6 |
| Journal | Computing and Visualization in Science |
| Volume | 8 |
| Issue number | 3-4 |
| Early online date | 1 Dec 2005 |
| Publication status | Published - Dec 2005 |
Abstract
We present new results from 11, 7, 12 on various Schwarz methods for the h and p versions of the boundary element methods applied to prototype first kind integral equations on surfaces. When those integral equations (weakly/hypersingular) are solved numerically by the Galerkin boundary element method, the resulting matrices become ill-conditioned. Hence, for an efficient solution procedure appropriate preconditioners are necessary to reduce the numbers of CG-iterations. In the p version where accuracy of the Galerkin solution is achieved by increasing the polynomial degree the use of suitable Schwarz preconditioners (presented in the paper) leads to only polylogarithmically growing condition numbers. For the h version where accuracy is achieved by reducing the mesh size we present a multi-level additive Schwarz method which is competitive with the multigrid method.
Keywords
- Boundary elements hp version, First kind integral equations, Preconditioners, Schwarz methods
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Computer Science(all)
- Software
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- General Engineering
- Computer Science(all)
- Computer Vision and Pattern Recognition
- Computer Science(all)
- Computational Theory and Mathematics
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In: Computing and Visualization in Science, Vol. 8, No. 3-4, 12.2005, p. 211-216.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Some schwarz methods for integral equations on surfaces-h and p versions
AU - Stephan, Ernst P.
AU - Maischak, Matthias
AU - Leydecker, Florian
PY - 2005/12
Y1 - 2005/12
N2 - We present new results from 11, 7, 12 on various Schwarz methods for the h and p versions of the boundary element methods applied to prototype first kind integral equations on surfaces. When those integral equations (weakly/hypersingular) are solved numerically by the Galerkin boundary element method, the resulting matrices become ill-conditioned. Hence, for an efficient solution procedure appropriate preconditioners are necessary to reduce the numbers of CG-iterations. In the p version where accuracy of the Galerkin solution is achieved by increasing the polynomial degree the use of suitable Schwarz preconditioners (presented in the paper) leads to only polylogarithmically growing condition numbers. For the h version where accuracy is achieved by reducing the mesh size we present a multi-level additive Schwarz method which is competitive with the multigrid method.
AB - We present new results from 11, 7, 12 on various Schwarz methods for the h and p versions of the boundary element methods applied to prototype first kind integral equations on surfaces. When those integral equations (weakly/hypersingular) are solved numerically by the Galerkin boundary element method, the resulting matrices become ill-conditioned. Hence, for an efficient solution procedure appropriate preconditioners are necessary to reduce the numbers of CG-iterations. In the p version where accuracy of the Galerkin solution is achieved by increasing the polynomial degree the use of suitable Schwarz preconditioners (presented in the paper) leads to only polylogarithmically growing condition numbers. For the h version where accuracy is achieved by reducing the mesh size we present a multi-level additive Schwarz method which is competitive with the multigrid method.
KW - Boundary elements hp version
KW - First kind integral equations
KW - Preconditioners
KW - Schwarz methods
UR - http://www.scopus.com/inward/record.url?scp=29044444798&partnerID=8YFLogxK
U2 - 10.1007/s00791-005-0011-8
DO - 10.1007/s00791-005-0011-8
M3 - Article
AN - SCOPUS:29044444798
VL - 8
SP - 211
EP - 216
JO - Computing and Visualization in Science
JF - Computing and Visualization in Science
SN - 1432-9360
IS - 3-4
ER -