A pseudospectral penalty scheme for 2D isotropic elastic wave computations

Journal of Scientific Computing

Volumn 33, Issue 3, 2007, Pages 313-348

  Feng, Ko An ^a   Teng, Chun Hao ^a   Chen, Min Hung ^a  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

Author keywords

Elastic waves; Multidomain schemes; Pseudospectral penalty methods; Velocity stress formulation

Indexed keywords

CURVILINEAR QUADRILATERAL DOMAINS; LEGENDRE PSEUDOSPECTRAL PENALTY SCHEME; PSEUDOSPECTRAL SCHEMES; TENSOR PRODUCT FORMULATIONS; VELOCITY STRESS FORMULATIONS;

BOUNDARY CONDITIONS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; TENSORS; WAVE EQUATIONS;

ELASTIC WAVES;

EID: 35548948031     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-007-9154-8     Document Type: Article

References (34)

1. Carcion, J.M.: The wave equation in generalized coordinates. Geophysics 59, 1911-1919 (1994)
2. Carcion, J.M.: A 2D Chebyshev differential operator for the elastic wave equation. Comput. Methods Appl. Mech. Eng. 130, 33-45 (1996)
3. Carpenter, M.H., Kennedy, C.A.: Fourth order 2N-storage Runge-Kutta scheme. NASA-TM-109112 (NASA Langley Research Center, VA) (1994)
4. Carpenter, M.H., Gottlieb, D.: Spectral methods on arbitrary grids. J. Comput. Phys. 129, 74-86 (1996)
5. Don, W.S., Gottlieb, D.: The Chebyshev-Legendre method: Implementing Legendre methods on Chebyshev points. SIAM J. Numer. Anal. 31, 1519-1534 (1994)
6. Dumbser, M., Käser, M.: An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes II. The three-dimension isotropic case. Geophys. J. Int. 167, 319-336 (2006)
7. Funaro, D., Gottlieb, D.: A new method of imposing boundary conditions in pseudospectral approximations of hyperbolic equations. Math. Comput. 51, 599-613 (1988)
8. Funaro, D., Gottlieb, D.: Convergence results for pseudospectral approximations of hyperbolic systems by a penalty-type boundary treatment. Math. Comput. 57, 585-596 (1991)
9. Gordon, W.J., Hall, C.A.: Transfinite element methods: Blending-function interpolation over arbitrary curved element domains. Numer. Math. 21, 109-129 (1973)
10. Gordon, W.J., Hall, C.A.: Construction of curvilinear co-ordinate systems and applications to mesh generations. Int. J. Numer. Methods Eng. 7, 461-477 (1973)
11. Gottlieb, D., Hesthaven, J.S.: Spectral methods for hyperbolic problems. J. Comput. Appl. Math. 128, 83-131 (2001)
12. Hesthaven, J.S.: A stable penalty method for the compressible Navier-Stokes equations II. One-dimensional domain decomposition schemes. SIAM J. Sci. Comput. 18, 658-685 (1997)
13. Hesthaven, J.S.: A stable penalty method for the compressible Navier-Stokes equations III. Multi dimensional domain decomposition schemes. SIAM J. Sci. Comput. 20, 63-92 (1999)
14. Hesthaven, J.S.: Spectral penalty methods. Appl. Numer. Math. 33, 23-41 (2000)
15. Hesthaven, J.S., Gottlieb, D.: A stable penalty method for the compressible Navier-Stokes equations I. Open boundary conditions. SIAM J. Sci. Comput. 17, 579-612 (1996)
16. Hesthaven, J.S., Gottlieb, D.: Stable spectral methods for conservation laws on triangles with unstructured grids. Comput. Methods Appl. Mech. Eng. 175, 361-381 (1999)
17. Hesthaven, J.S., Rasmussen, J.J., Bergè, L., Wyller, J.: Numerical studies of localized wave fields governed by the Raman-extended derivative nonlinear Schrödinger equation. J. Phys. A: Math. Gen. 30, 8207-8224 (1997)
18. Hesthaven, J.S., Teng, C.H.: Stable spectral methods on tetrahedral elements. SIAM J. Sci. Comput. 21, 2353-2380 (2000)
19. Hesthaven, J.S., Warburton, T.: Nodal high-order methods on unstructured grids I. Time-domain solution of Maxwell's equations. J. Comput. Phys. 181, 186-221 (2002)
20. Igel, H.: Wave propagation in three-dimensional spherical sections by the Chebyshev spectral method. J. Comput. Phys. 57, 585-596 (1999)
21. Käser, M., Dumbser, M.: An arbitray high-order discontinuous Galerkin method for elastic waves on unstructured meshes-I. The two-dimensional isotropic case with external source terms. Geophys. J. Int. 166, 855-877 (2006)
22. Käser, M., Dumbser, M., Puente, J., Igel, H.: An arbitray high-order discontinuous Galerkin method for elastic waves on unstructured meshes-III. Viscoelastic attenuation. Geophys. J. Int. 168, 224-242 (2007)
23. Komatitsch, D., Tromp, J.: Introduction to the spectral-element method for 3-D seismic wave propagation. Geophys. J. Int. 139, 806-822 (1999)
24. Komatitsch, D., Tromp, J.: Spectral-element simulations of global seismic wave propagation-I. Validation. Geophys. J. Int. 149, 390-412 (2002)
25. Komatitsch, D., Vilotte, J.P.: The spectral-element method: An efficients tool to simulate the seismic response of 2D and 3D geological structures. Bull. Seismol. Soc. Am. 88, 368-392 (1998)
26. Nielsen, S.A., Hesthaven, J.S.: A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries. Ultrasonics 40, 177-180 (2002)
27. Priolo, E., Carcione, J.M., Seriani, G.: Numerical simulation of interface waves by high-order spectral modeling techniques. J. Acoust. Soc. Am. 95, 681-693 (1994)
28. Zeng, Y.Q., Liu, Q.H.: A multidomain PSTD method for 3D elastic wave equations. Bull. Seismol. Soc. Am. 94, 1002-1015 (2004)
29. Achenbach, J.D.: Wave Propagation in Elastic Solids. North-Holland/ Elsevier, Amsterdam/New York (1973)
30. Brekhovskikh, L.M., Goncharov, V.: Mechanics of Continua and Wave Dynamics, 2nd edn. Springer Series on Wave Phenomena, vol. 1. Springer, New York (1994)
31. Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods in Fluid Dynamics. Springer Series in Computational Physics. Springer, New York (1986)
32. Funaro, D.: Polynomial Approximation of Differential Equations. Springer, New York (1992)
33. Funaro, D., FORTRAN routines for spectral methods. Available with software at: http://cdm.unimo.it/home/matematica/funaro.daniele/rout.htm
34. Funaro, D.: Spectral Elements for Transport-Dominated Equations. Springer, New York (1997)