An iterative defect-correction type meshless method for acoustics

International Journal for Numerical Methods in Engineering

Volumn 57, Issue 15, 2003, Pages 2131-2146

  Lacroix, V ^a   Bouillard, Ph ^a   Villon, P ^b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Acoustics; Dispersion error; Element free Galerkin method; Helmholtz equation; Meshless method

Indexed keywords

ACOUSTIC WAVE PROPAGATION; BOUNDARY CONDITIONS; COMPUTER SIMULATION; FREQUENCIES; GALERKIN METHODS;

MESHLESS METHOD;

ACOUSTICS;

ACOUSTICS; MATHEMATICAL METHOD; MATHEMATICAL MODELING; WAVE PROPAGATION;

EID: 0041422343     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.757     Document Type: Article

References (32)

1. Deraemaeker A, Babuška I, Bouillard Ph. Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions. International Journal for Numerical Methods in Engineering 1999; 46:471-500.
2. Bouillard Ph. Méthodes de contrôle de la qualité de solutions éléments finis (application à l'acoustique). Thèse de doctorat, Service des Milieux Continus, Université Libre de Bruxelles, 1997.
3. Bouillard Ph, Ihlenburg F. Error estimation and adaptivity for the finite element method in acoustics. Advances in Adaptive Computational Methods in Mechanics 1998; 477-492.
4. Ihlenburg F, Babuška I. Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation. International Journal for Numerical Methods in Engineering 1995; 38:3745-3774.
5. Zienkiewicz OC. Achievements and some unsolved problems of the finite element method. International Journal for Numerical Methods in Engineering 2000; 47:9-28.
6. Harari I, Hughes TJR. Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains. Computer Methods in Applied Mechanics and Engineering 1992; 98(3):411-454.
7. Babuška I, Ihlenburg F, Paik E. A generalized finite element method for solving the Helmholtz equation in two dimension with minimal pollution. Computer Methods in Applied Mechanics and Engineering 1995; 128: 325-359.
8. Franca L, Farhat C, Macedo A. Residual-free bubbles for the Helmholtz equation. International Journal for Numerical Methods in Engineering 1997; 40:4003-4009.
9. Deraemaeker A, Babuška I, Bouillard Ph. Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions. International Journal for Numerical Methods in Engineering 1999; 46:471-500.
10. Hughes TJR. Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origins of stabilized methods. Computer Methods in Applied Mechanics and Engineering 1995; 127:387-401.
11. Brandt A, Livshits I. Wave-ray multigrid method for standing wave equation. Electronic Transactions on Numerical Analysis 1997; 6:162-181.
12. Gerdes K, Demkowicz L. Solution of the 3D Helmholtz equation in arbitrary exterior domains using hp-FEM and IFEM. Computer Methods in Applied Mechanics and Engineering 1996; 137:239-273.
13. Uras RA, Chang CT, Chen Y, Liu WK. Multiresolution reproducing kernel particle methods in acoustics. Journal of Computational Acoustics 1997; 5(1):71-94.
14. Voth ThE, Christon MA. Discretization errors associated with reproducing kernel methods: one-dimensional domains. Computer Methods in Applied Mechanics and Engineering 2001; 190(18-19):2429-2446.
15. Suleau S, Bouillard Ph. ID dispersion analysis for the element-free Galerkin method for the Helmholtz equation. International Journal for Numerical Methods in Engineering 2000; 47:1169-1188.
16. Suleau S, Deraemaeker A, Bouillard Ph. Dispersion and pollution of meshless solutions for the Helmholtz equation. Computer Methods in Applied Mechanics and Engineering 2000; 190:639-657.
17. Babuška I, Melenk J. The partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40:727-758.
18. Chadwick E, Bettes P. Modelling of progressive short waves using wave envelopes. International Journal for Numerical Methods in Engineering 1997; 40:3229-3245.
19. Farhat C, Harari I, Franca LP. A discontinuous finite element method for the Helmholtz equation. Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), Barcelona, Spain, 11-14 September 2000.
20. Lacroix V, Bouillard Ph, Villon P. Iterative multilevel meshless method for acoustics. Proceedings of the Sixth U.S. National Congress on Computational Mechanics (USNCCM), Dearborn, Michigan, USA, 1-4 August 2001.
21. Lancaster P, Salkausas K. Surfaces generated by moving least squares methods. Mathematics of Computation 1981; 37:141-158.
22. Nayroles B, Touzot G, Villon P. Generalizing the FEM: diffuse approximation and diffuse elements. Computational Mechanics 1992; 10:307-318.
23. Belytschko T, Lu YY, Gu L. Element-free Galerkin Methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
24. Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P. Meshless methods: an overview and recent developments. Computer Methods in Applied Mechanics and Engineering 1996; 139:3-47.
25. Suleau St, Bouillard Ph. Accurate acoustic computations using a meshless method. Computer Assisted Mechanics and Engineering Science 2001; 8:445-468.
26. Kaljevic I, Saigal S. An improved element free Galerkin formulation. International Journal for Numerical Methods in Engineering 1997; 40:2953-2974.
27. Krongauz Y, Belytschko T. Enforcement of essential boundary conditions in meshless approximations using finite elements. Computer Methods in Applied Mechanics and Engineering 1996; 131:133-145.
28. Gavete L, Falcon S, Bellido JC. Dirichlet boundary condition in element free Galerkin method. Proceedings of ECCOMAS. Barcelona, Spain, 11-14 September 2000.
29. Mukherjee YX, Mukherjee S. On boundary conditions in the element free Galerkin method. Computational Mechanics 1997; 19:264-270.
30. Bouillard Ph, Suleau S. Element-free Galerkin solutions for Helmholtz problems: formulation and numerical assessment of the pollution effect. Computer Methods in Applied Mechanics and Engineering 1998; 162: 317-335.
31. SYSNOISE User Manual. LMS International, Researchpark ZI, Interleuvenlaan, 68, 3001 Leuven, Belgium.
32. Nefske DJ. Sound in small enclosures. In Noise and Vibration Control Engineering. Principles and Applications (1st edn), Beranek L, Vér I (eds). Wiley: Chichester, 1992, ISBN 0-471-61751-2.