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.
|Number of pages||15|
|Journal||Applied Numerical Mathematics|
|Publication status||Published - Mar 2001|