Analysis of wave propagation in 1D inhomogeneous media

Numerical Functional Analysis and Optimization

Volumn 27, Issue 1, 2006, Pages 25-55

  Guidotti, Patrick ^a   Solna, Knut ^a   Lambers, James V ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Inhomogeneous media; Krylov subspace spectral method; Propagator; Spectral asymptotics; Wave equation

Indexed keywords

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; NATURAL FREQUENCIES; NUMERICAL METHODS; WAVE EQUATIONS;

INHOMOGENEOUS MEDIA; KRYLOV SUBSPACE SPECTRAL METHOD; PROPAGATOR; SPECTRAL ASYMPTOTICS; WAVE EQUATION;

WAVE PROPAGATION;

EID: 33645005114     PISSN: 01630563     EISSN: 15322467     Source Type: Journal    
DOI: 10.1080/01630560500538763     Document Type: Article

References (17)

1. A. Bensoussan, J. L. Lions, and G. Papanicolaou (1978). Asymptotic Analysis of Periodic Structures. North Holland, Amsterdam.
2. P. G. Casazza (2000). The art of frame theory Taiwanese J. Math. 4(2):129-201.
3. N. Dunford and J. T. Schwarz (1971). Linear Operators, Part III. Wiley, New York.
4. G. Dahlquist, S. C. Eisenstat, and G. H. Golub (1972). Bounds for the error of linear systems of equations using the theory of moments. J. Math. Anal. Appl. 37:151-166.
5. G. H. Golub (1974). Bounds for matrix moments. Rocky Mt. J. Math. 4:207-211.
6. G. H. Golub (1973). Some modified matrix eigenvalue problems. SIAM Rev. 15:318-334.
7. G. H. Golub and C. Meurant (1993). Matrices, Moments, and Quadrature. Stanford University Technical Report SCCM-93-07.
8. G. H. Golub and J. Welsch (1969). Calculation of Gauss quadrature rules. Math. Comp. 23:221-230.
9. B. Gustafsson, H.-O. Kreiss, and J. Oliger (1955). Time-Dependent Problems and Difference Methods. Wiley, New York.
10. J. B. Keller, D. McLaughlin, and G. Papanicolaou (1995). Surveys in Applied Mathematics. Plenum Press, New York.
11. H.-O. Kreiss, N. A. Petersson, and J. Yström (2002). Difference approximations for the second order wave equation. SIAM J. Numer. Anal. 40:1940-1967.
12. J. V. Lambers (2003). Krylov subspace methods for variable-coefficient initial-boundary value problems. Ph.D. Thesis, Stanford University SCCM Program.
13. J. V. Lambers. Practical Implementation of Krylov Subspace Spectral Methods (submitted).
14. G. Milton (2002). The theory of composites. Cambridge Monographs on Applied and Computational Mathematics 6:xxviii,720.
15. K. Sølna and G. Milton (2002). Can mixing materials make electromagnetic signals travel faster? SIAM J. App. Math. V62 (6):2064-2091.
16. G. Szego (1974). Orthogonal Polynomials, 3rd. ed. American Mathematical Society, Providence, RI.
17. Yu. Safarov and D. Vassiliev (1997). The Asymptotic Distributions of Eigenvlaues of Partial Differential Operators. Translation of Mathematical Monographs, AMS.