A numerical integration scheme for special quadrilateral finite elements for the Helmholtz equation. (English) Zbl 1016.65087
Summary: This paper is an extension to an earlier paper of P. Bettess, O. Laghrouche, J. Shirron, B. Peseux, R. Sugimoto and J. Trevelyan [A numerical integration scheme for special finite elements for the Helmholtz equation, Int. J. Numer. Meth. Eng. (to appear)] dealing with the general problem of integrating special wave elements and specifically deals with quadrilateral elements, which have their own unique problems. The theory for integrating quadrilateral wave finite 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.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
Keywords:
short waves; finite elements; special finite elements; semi-analytical integration; numerical integration; Helmholtz equation; Gauss-Legendre integrationReferences:
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