Rapid zonal algorithm for polyelliptic PDEs in domains with high aspect ratio

Presented herein is a zonal boundary element method (ZBEM) for the rapid an d efficient solution of a wide class of polyelliptic boundary value problem s which can be recast in integral-equation form, in domains with high aspec t ratio (L >> 1). In contrast to the dense-matrix solution procedure of the classical BEM (CBEM), the ZBEM employs a sparse, block-tridiagonal matrix solution technique which admits rapid inversion. Our large-L asymptotic the ory predicts the ZBEM to be O(L-2) times faster than, and require O(L-1) ti mes the storage of, the equivalent-resolution CBEM. By implementing the ZBE M on two engineering-based harmonic and biharmonic example boundary value p roblems, up to L = 1000, we are able to demonstrate excellent agreement bet ween our numerical results and our asymptotic theory. We suggest that the Z BEM permits the economical solution of a wide class of problems which were hitherto resolvable on only the largest computational platforms. (C) 2000 E lsevier Science Ltd. All rights reserved.