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SUMMARYIn the present paper a new adaptive successive over relaxation domain decomposition technique is developed for the boundary spectral strip method. The proposed scheme is based on dividing the overall domain of the problem into several subdomains. First each of the subdomains in the BIEM matrices is analysed independently. These matrices together with an arbitrary initial guess of displacements on the interface of each two neighbouring subdomains, enable an iterative and a very efficient solution of the whole problem. An adaptive procedure, based on comparing two norms along the interface of subregions, is carried out to impose successive over relaxation convergence. Numerical results comparing the present scheme with single domain solutions emphasize the capability of the proposed technique regarding accuracy and computational efforts.1997 by John Wiley & Sons, Ltd.

A new spectral Galerkin formulation is presented for the solution of boundary integral equations. The formulation is carried out with an exact singularity subtraction procedure based on analytical integrations, which provides a fast and precise way to evaluate the coefficient matrices. The new Galerkin formulation is based on the exact geometry of the problem boundaries and leads to a non-element method that is completely free of mesh generation. The numerical behaviour of the method is very similar to the collocation method; for Dirichlet problems, however, it leads to a symmetric coefficient matrix and therefore requires half the solution time of the collocation method.