Fast BEM-solution of Laplace problems with H-matrices and ACA

The main problems for applying boundary element methods (BEM) in computational electromagnetism are related to the large memory requirements of the matrices and the convergence of the iterative solver. In this paper, we solve a Laplace problem with mixed boundary conditions by making use of a variat...

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Bibliographic Details
Published inIEEE transactions on magnetics Vol. 42; no. 4; pp. 627 - 630
Main Authors Ostrowski, J., Andjelic, Z., Bebendorf, M., Cranganu-Cretu, B., Smajic, J.
Format Journal Article Conference Proceeding
LanguageEnglish
Published New York, NY IEEE 01.04.2006
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algebra
Approximation
Boundary conditions
Boundary element method
Boundary element methods
boundary element methods (BEM)
boundary integral equations
Conductors
Convergence
Cross-disciplinary physics: materials science; rheology
Current density
data compression
Discretization
Exact sciences and technology
Geometry
Integral equations
Iterative methods
Laplace equations
Magnetism
Materials science
Mathematical analysis
Matrices
Matrix methods
Other topics in materials science
Physics
Solvers
stability
symbol manipulation
Symmetric matrices
Proceedings
boundary integral equations
data compression
Stability
Algebra
Integral equations
symbol manipulation
boundary element methods (BEM)
Calculus
Boundary element method
Magnetic properties
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Summary:The main problems for applying boundary element methods (BEM) in computational electromagnetism are related to the large memory requirements of the matrices and the convergence of the iterative solver. In this paper, we solve a Laplace problem with mixed boundary conditions by making use of a variational symmetric direct boundary integral equation. The Galerkin discretization results in densely populated matrices that are here compressed by adaptive cross approximation. This leads to an approximation of the underlying BEM-operator by means of so-called hierarchical matrices (H-Matrices). These matrices are then used to construct an effective preconditioner for the iterative solver. Numerical experiments demonstrate the application of the method
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0018-9464
1941-0069
DOI:10.1109/TMAG.2006.871642