A numerical integration scheme for special finite elements for the Helmholtz equation
| Autor: | Bernard Peseux, Peter Bettess, Jon Trevelyan, Omar Laghrouche, Rie Sugimoto, Joseph J. Shirron |
|---|---|
| Přispěvatelé: | Durham University, Naval Research Laboratory (NRL), Institut de Recherche en Génie Civil et Mécanique (GeM), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2002 |
| Předmět: |
Helmholtz equation
Fortran Computation MathematicsofComputing_NUMERICALANALYSIS 010103 numerical & computational mathematics 01 natural sciences [SPI.MECA.MEMA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of materials [physics.class-ph] ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION special finite elements semi-analytical integration 0101 mathematics Mathematics computer.programming_language Extended finite element method Numerical Analysis Quadrilateral Applied Mathematics Mathematical analysis General Engineering Mixed finite element method short waves Finite element method Numerical integration 010101 applied mathematics numerical integration finite elements partition of unity method computer |
| Zdroj: | Heriot-Watt University International Journal for Numerical Methods in Engineering International Journal for Numerical Methods in Engineering, Wiley, 2003, 56 (4), pp.531-552. ⟨10.1002/nme.575⟩ |
| ISSN: | 1097-0207 0029-5981 |
| DOI: | 10.1002/nme.575 |
| Popis: | International audience; 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 abscissae 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Plný text