3D multidomain BEM for solving the Laplace equation

An efficient 3D multidomain boundary element method (BEM) for solving problems governed by the Laplace equation is presented. Integral boundary equations are discretized using mixed boundary elements. The field function is interpolated using a continuous linear function while its derivative in a nor...

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Bibliographic Details
Published in:Engineering analysis with boundary elements 2007-06, Vol.31 (6), p.528-538
Main Authors: RAMSAK, Matjaz, SKERGET, Leopold
Format: Article
Language:English
Subjects:
Boundary element method
Boundary-integral methods
Computational techniques
Derivatives
Exact sciences and technology
Finite element method
Fluid dynamics
Fundamental areas of phenomenology (including applications)
General theory
Laplace equation
Mathematical analysis
Mathematical methods in physics
Mathematical models
Matrices
Mixed boundary elements
Multidomain method
Physics
Potential flow
Three dimensional
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Summary:An efficient 3D multidomain boundary element method (BEM) for solving problems governed by the Laplace equation is presented. Integral boundary equations are discretized using mixed boundary elements. The field function is interpolated using a continuous linear function while its derivative in a normal direction is interpolated using a discontinuous constant function over surface boundary elements. Using a multidomain approach, also known as the subdomain technique, sparse system matrices similar to the finite element method (FEM) are obtained. Interface boundary conditions between subdomains leads to an over-determined system matrix, which is solved using a fast iterative linear least square solver. The accuracy and robustness of the developed numerical algorithm is presented on a scalar diffusion problem using simple cube geometry and various types of meshes. Efficiency is demonstrated with potential flow around the complex geometry of a fighter airplane using tetrahedral mesh with over 100,000 subdomains on a personal computer.
ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2006.10.006