Efficient preconditioners for iterative solution of the boundary element equations for the three-dimensional Helmholtz problem
Chen, K. and Harris, P. (2001) Efficient preconditioners for iterative solution of the boundary element equations for the three-dimensional Helmholtz problem Applied Numerical Mathematics, 36 (4). pp. 475-489. ISSN 0168-9274
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In this paper two types of local sparse preconditioners are generalized to solve three-dimensional Helmholtz problems iteratively. The iterative solvers considered are the conjugate gradient normal method (CGN) and the generalized minimal residual method (GMRES). Both types of preconditioners can ensure a better eigenvalue clustering for the normal equation matrix and thus a faster convergence of CGN. Clustering of the eigenvalues of the preconditioned matrix is also observed. We consider a general surface configuration approximated by piecewise quadratic elements defined over unstructured triangular partitions. We present some promising numerical results.
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