Investigation of a three-dimensional spectral element method for Helmholtz's equation

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2668, Issue , 2003, Pages 819-825

  Mehdizadeh, Omid Z ^a   Paraschivoiu, Marius ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b Dept of Electrical and Computer Engineering   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTICS; NUMERICAL METHODS;

COMPLEX GEOMETRIES; COMPUTATIONAL COSTS; EFFICIENT NUMERICAL METHOD; GALERKIN FINITE ELEMENTS; HIERARCHICAL BASIS; HIGH WAVE NUMBER; SPECTRAL ELEMENT METHOD; TETRAHEDRAL ELEMENTS;

FINITE ELEMENT METHOD;

EID: 24744448484     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44843-8_89     Document Type: Article

References (19)

1. Tezaur, R., Macedo, A., Farhat, C., Djellouli, R.: Three-Dimensional Finite Element Calculations in Acoustic Scattering Using Arbitrarily Shaped Convex Artificial Boundaries. Int. J. Num. Meth. Eng. 53(6) (2002) 1461-1476
2. Ramakrishnan, R., Watson, W.R.: Design Curves for Rectangular Splitter Silencers. Appl. Acoust J. 35 (1992) 1-24
3. Manolis, G.D., Shaw, R.P.: Harmonic Wave Propagation through Viscoelastic Heterogeneous Media Exhibiting Mild Stochasticity - I. Fundamental Solutions. Soil Dynam. Earthq. Eng. 15(2) (1996) 119-127
4. Ratowsky, R.P., Fleck Jr., J.A., Feit, M.D.: Helmholtz Beam Propagation in Rib Waveguides and Couplers by Iterative Lanczos Reduction. Opt. Soc. Amer. A 9 (1992) 256
5. Junger, M.C., Feit, D.: Sound, Structures and Their Interaction. 2nd edition MIT Press Cambridge MA (1986)
6. Kashiyama, K., Sakuraba, M.: Adaptive Boundary-Type Finite Element Method for Wave Diffraction-Reflection in Harbours. Comput Meth. Appl. Mech. Eng. 112 (1994) 185-197
7. Stewart, J.R., Hughes, T.J.R.: Explicit Residual-Based a Posteriori Error Estimation for Finite Element Discretizations of the Helmholtz Equation: Computation of the Constant and New Measures of Error Estimator Quality. Comput. Meth. Appl. Mech. Eng. 131(3-4) (1996) 335-363
8. Shaw, R.P.: Integral Equation Methods in Acoustics. Boundary Elements X Vol. 4 C.A. Brebbia (ed.) Springer Berlin (1988) 221-244
9. Copely, L.G.: Fundamental Results Concerning Integral Representations in Acoustic Radiation. J. Acoust. Soc. Amer. 44(1) (1968) 28-32
10. Harari, I., Hughes, T.J.R.: Finite Element Methods for the Helmholtz Equation in an Exterior Domain: Model Problems. Comput. Meth. Appl. Mech. Eng. 87(1) (1991) 59-96
11. Givoli, D., Harari, I. (eds): Exterior Problems of Wave Propagations (Special Issue). Comput Meth. Appl. Mech. Eng. 164(1-2) (1998) 1-2
12. Harari, I., Hughes, T.J.R.: A Cost Comparison of Boundary Element and Finite Element Methods for Problems of Time-Harmonic Acoustics. Comput. Meth. Appl, Mech. Eng. 97 (1992) 77-102
13. Babuska, I., Ihlenburg, F., Paik, E.T., Sauter, S.A.: A Generalized Finite Element Method for Solving the Helmholtz Equation in Two Dimensions with Minimal Pollution. Comput. Meth. Appl. Mech. Eng. 128(3-4) (1995) 325-359
14. Thompson, L.L., Pinsky, P.M.: A Galerkin Least-squares Finite Element Method for the Two-Dimensional Helmholtz Equation. Int. J. Num. Meth. Eng. 38(3) (1995) 371-397
15. Ihlenburg, F., Babuska, I.: Finite Element Solution of the Helmholtz Equation with High Wave Number. Part I: The h-version of the FEM. Comput. Math. Appl. 30(9) (1995) 9-37
16. Harari, I., Hughes, T.J.R.: Galerkin/least-squares Finite Element Methods for the Reduced Wave Equation with Nonreflecting Boundary Conditions in Unbounded Domains, Comput. Meth. Appl. Mech. 98(3) (1992) 411-454
17. Harari, I., Nogueria, C.L.: Reducing Dispersion of Linear Triangular Elements for the Helmholtz Equation. J. Eng. Mech. 128(3) (2002) 351-358
18. Whiting C.H., Jansen K.E.: A Stabilized Finite Element Method for the Incompressible Navier-Stokes Equations using a Hierarchical Basis. Int. J. Numer. Meht Fluids 35 (2001) 93-116.
19. Kamiadakis, G.M., Sherwin, S.J.: Spectral/hp Element Methods for CFD. Oxford University Press Oxford (1999)