Abstract
In this article, a reverse contribution technique is proposed to accelerate the construction of the dense
influence matrices associated with a Galerkin approximation of singular and hypersingular boundary integral equations of mixed-type in potential theory. In addition, a general-purpose sparse preconditioner for boundary
element methods has also been developed to successfully deal with ill-conditioned linear systems arising from the
discretization of mixed boundary-value problems on non-smooth surfaces. The proposed preconditioner, which originates from the precorrected-FFT method, is sparse, easy to generate and apply in a Krylov subspace iterative solution of discretized boundary integral equations. Moreover, an approximate inverse of
the preconditioner is implicitly built by employing an incomplete LU factorization.
Numerical experiments involving mixed boundary-value problems for the Laplace equation are included to illustrate
the performance and validity of the proposed techniques.