The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling. (English) Zbl 0947.65125

Ainsworth, Mark; McLean, William; Tran, Thanh

SIAM J. Numer. Anal. 36, No. 6, 1901-1932 (1999).

The authors consider the Galerkin boundary element method applied to weakly singular and hypersingular integral equations based on a discretization by standard nodal basis functions with respect to a locally refined mesh. To cope with the possibly badly conditioned stiffness matrix, they suggest a diagonal preconditioner formed from the entries on the diagonal of the stiffness matrix. That diagonal scaling results in a condition number of the preconditioned system comparable to that for a uniform partition.

Reviewer: R.H.W.Hoppe (München)

MSC:

65N38	Boundary element methods for boundary value problems involving PDEs
65N50	Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
45E10	Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
65R20	Numerical methods for integral equations
35J25	Boundary value problems for second-order elliptic equations
65F35	Numerical computation of matrix norms, conditioning, scaling

Keywords:

Galerkin boundary element method; locally refined meshes; preconditioning; weakly singular and hypersingular integral equations; condition number