SUMMARYThe theory for integrating the element matrices for rectangular, triangular and quadrilateral ÿnite elements for the solution of the Helmholtz equation for very short waves is presented. A numerical integration scheme is developed. Samples of Maple and Fortran code for the evaluation of integration absciss and weights are made available. The results are compared with those obtained using large numbers of Gauss-Legendre integration points for a range of testing wave problems. The results demonstrate that the method gives correct results, which gives conÿdence in the procedures, and show that large savings in computation time can be achieved.

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SUMMARYThis paper is an extension to an earlier paper dealing with the general problem of integrating special wave elements and speciÿcally deals with quadrilateral elements, which have their own unique problems. The theory for integrating quadrilateral wave ÿnite elements for the solution of the Helmholtz equation for very short waves is presented. The results are compared with those obtained using large numbers of Gauss-Legendre integration points.

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