EFFICIENT PRECONDITIONERS for
ITERATIVE SOLUTION of THE BOUNDARY ELEMENT EQUATIONS for THE 
               THREE DIMENSIONAL HELMHOLTZ EQUATION 

                Ke Chen

               Department of Mathematical Sciences 
               University of Liverpool
               Peach Street, Liverpool L69 7ZL, UK.
                     http://www.liv.ac.uk/maths/applied/

               Paul J. Harris
               School of Computing and Mathematical Sciences 
               University of Brighton 
               Lewes Road, Brighton BN2 4GJ, UK.
                     http://www.it.bton.ac.uk/cms/

------------------------------- Abstract ----------------------------------

In this paper two types of local sparse preconditioners are generalised to
solve three-dimensional Helmholtz problems iteratively.
The iterative solvers considered are
 the conjugate gradient normal method (CGN) and
the generalised 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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                                  copyright JANM (APNUM ISSN 0168-9274)