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A numerical integration scheme for special finite elements for the Helmholtz equation
Author(s) -
Bettess Peter,
Shirron Joseph,
Laghrouche Omar,
Peseux Bernard,
Sugimoto Rie,
Trevelyan Jon
Publication year - 2002
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.575
Subject(s) - quadrilateral , finite element method , fortran , helmholtz equation , scheme (mathematics) , numerical integration , computation , gauss , legendre polynomials , mathematics , range (aeronautics) , mathematical analysis , computer science , algorithm , structural engineering , engineering , boundary value problem , physics , quantum mechanics , aerospace engineering , operating system
The theory for integrating the element matrices for rectangular, triangular and quadrilateral finite 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 abscissæ 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 confidence in the procedures, and show that large savings in computation time can be achieved. Copyright © 2002 John Wiley & Sons, Ltd.