On the Implementation of 3D Galerkin Boundary Integral Equations
- ORNL
In this article, a reverse contribution technique is proposed to accelerate the construction of the dense influence matrices associated with a Galerkin approximation of singular and hypersingular boundary integral equations of mixed-type in potential theory. In addition, a general-purpose sparse preconditioner for boundary element methods has also been developed to successfully deal with ill-conditioned linear systems arising from the discretization of mixed boundary-value problems on non-smooth surfaces. The proposed preconditioner, which originates from the precorrected-FFT method, is sparse, easy to generate and apply in a Krylov subspace iterative solution of discretized boundary integral equations. Moreover, an approximate inverse of the preconditioner is implicitly built by employing an incomplete LU factorization. Numerical experiments involving mixed boundary-value problems for the Laplace equation are included to illustrate the performance and validity of the proposed techniques.
- Research Organization:
- Oak Ridge National Laboratory (ORNL)
- Sponsoring Organization:
- SC USDOE - Office of Science (SC)
- DOE Contract Number:
- AC05-00OR22725
- OSTI ID:
- 979210
- Journal Information:
- Engineering Analysis with Boundary Elements, Journal Name: Engineering Analysis with Boundary Elements Journal Issue: 1 Vol. 34; ISSN 0955-7997
- Country of Publication:
- United States
- Language:
- English
Similar Records
Fast Galerkin BEM for 3D Potential Theory
Semi-analytic treatment of the three-dimensional Poisson equation via a Galerkin BIE method
Related Subjects
99 GENERAL AND MISCELLANEOUS
APPROXIMATIONS
BOUNDARY ELEMENT METHOD
BOUNDARY-VALUE PROBLEMS
FACTORIZATION
Galerkin approximation
IMPLEMENTATION
INTEGRAL EQUATIONS
LAPLACE EQUATION
PERFORMANCE
boundary element method
hypersingular integrals
incomplete LU
iterative methods
potential theory
singular integrals
sparse preconditioner
triangular boundary