Stability of a Chebychev pseudospectral solution of the wave equation with absorbing boundaries

Journal of Computational and Applied Mathematics

Volumn 87, Issue 2, 1997, Pages 243-259

  Renaut, Rosemary ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Absorbing boundaries; Pseudospectral Chebychev; Pseudospectrum; Stability; Wave equation

Indexed keywords

ACOUSTIC WAVE PROPAGATION; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CHEBYSHEV APPROXIMATION; CONVERGENCE OF NUMERICAL METHODS; EQUATIONS OF MOTION; FINITE DIFFERENCE METHOD; MATHEMATICAL OPERATORS; SPECTRUM ANALYSIS;

ABSORBING BOUNDARIES; DIRICHLET BOUNDARY; PSEUDOSPECTRAL CHEBYCHEV;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0031373157     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(97)00192-1     Document Type: Article

References (16)

1. C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods in Fluid Dynamics, Springer, New York, 1987.
2. F. Chaitin-Chatelin, Is nonnormality a serious difficulty?, CERFACS Report TR/PA/94/18.
3. R. Clayton, B. Engquist, Absorbing boundary conditions for acoustic and elastic wave equations, Bull. Seis. Soc. Am. 67 (1977) 1524-1540.
4. T.A. Driscoll, L.N. Trefethen, Pseudospectra of the wave operator with an absorbing boundary, J. Comput. Appl. Math. 69 (1996) 125-142.
5. B. Engquist, A. Majda, Radiation boundary conditions for acoustic and elastic wave calculations, Comm. Pure Appl. Math. 32 (1979) 313-357.
6. R.L. Higdon, Numerical absorbing boundary conditions for the wave equation, Math. Comput. 49 (1987) 65-90.
7. R. Kosloff, D. Kosloff, Absorbing boundaries for wave propagation problems, J. Comput. Phys. 63 (1986) 363-376.
8. -1) time step restriction, J. Comput. Phys. 104 (1993) 457-469.
9. L.J. Little, B.D. Welfert, Preconditioning of non-symmetric Stokes problems, preprint, Arizona State University, 1997.
10. S.C. Reddy, L.N. Trefethen, Lax stability of fully discrete spectral methods via stability regions and pseudoeigenvalues, Comput. Meth. Appl. Mech. Eng. 80 (1990) 147-164.
11. S.C. Reddy, L.N. Trefethen, Stability of the method of lines, Numer. Math. 62 (1992) 235-267.
12. R.A. Renaut, J. Fröhlich, A pseudospectral Chebychev method for the 2D wave equation with domain sketching and absorbing boundary conditions, J. Comput. Phys. 124 (1996) 324-336.
13. J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Wadsworth and Brooks/Cole, California, 1989.
14. L.N. Trefethen, Lax-stability vs. eigenvalue stability of spectral methods, in: K.W. Morton, M.J. Baines (Eds.), Numerical Methods for Fluid Dynamics III, Clarendon Press, Oxford, 1988.
15. L.N. Trefethen, Pseudospectra of matrices, in: D.F. Griffiths, C.A. Watson (Eds.), Numerical Analysis 1991, Longman, White Plains, NY, 1992.
16. J.C. Weiderman, L.N. Trefethen, The eigenvalues of second-order spectral differentiation matrices, SIAM J. Numer. Anal. 25 (1988) 1279-1298.