Preconditioning for Boundary Integral Equations
Copyright policy )Preconditioning for Boundary Integral Equations
This paper discusses three alternative preconditioning techniques to solve 3-D, mixed boundary conditions, Laplace equation problems. The direct boundary element equations are tested in conjunction with three iterative solution methods; namely, conjugate gradient on the normal equations, CGS of \textit{P. Sonneveld} [SIAM J. Sci. Stat. Comput. 10, No. 1, 36-52 (1989; Zbl 0666.65029)] and GMRES of \textit{Y. Saad} and \textit{M. H. Schultz} [ibid. 7, 856-869 (1986; Zbl 0599.65018)]. Emphasis is given to the condition number reduction and test examples indicate the improvement obtained by the alternative procedures. The paper is highly recommended to those working on this important field of improving solvers for dense and unsymmetric systems of equations arising from the boundary element method.
Iterative numerical methods for linear systems, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Integral representations of solutions to PDEs, Boundary element methods for boundary value problems involving PDEs, Laplace equation, Numerical methods for integral equations, test examples, preconditioning, boundary integral equations, boundary element equations, conjugate gradient, iterative solution, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), condition number reduction
Iterative numerical methods for linear systems, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Integral representations of solutions to PDEs, Boundary element methods for boundary value problems involving PDEs, Laplace equation, Numerical methods for integral equations, test examples, preconditioning, boundary integral equations, boundary element equations, conjugate gradient, iterative solution, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), condition number reduction
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