An embedded boundary method for the wave equation with discontinuous coefficients

SIAM Journal on Scientific Computing

Volumn 28, Issue 6, 2006, Pages 2054-2074

  Kreisst, Heinz Otto ^a   Petersson, N Anders ^b  

^a Träskö Storö Institute of Mathematics   (Sweden)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Discontinuous coefficients; Embedded boundary; Finite differences; Jump condition; Wave equation

Indexed keywords

BOUNDARY CONDITIONS; ELECTROMAGNETIC WAVE SCATTERING; EMBEDDED SYSTEMS; FINITE DIFFERENCE METHOD; NUMERICAL METHODS; STABILIZATION;

CARTESIAN GRID; DISCONTINUOUS COEFFICIENTS; EMBEDDED BOUNDARY; JUMP CONDITIONS;

WAVE EQUATIONS;

EID: 36349030356     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/050641399     Document Type: Article

References (28)

1. H.-O. KREISS, N. A. PETERSSON, AND J. YSTRÖM, Difference approximations for the second order wave equation, SIAM J. Numer. Anal., 40 (2002), pp. 1940-1967.
2. H.-O. KREISS, N. A. PETERSSON, AND J. YSTRÖM, Difference approximations of the Neumann problem for the second order wave equation, SIAM J. Numer. Anal., 42 (2004), pp. 1292-1323.
3. H.-O. KREISS AND N. A. PETERSSON, A second order accurate embedded boundary method for the wave equation with Dirichlet data, SIAM J. Sci. Comput., 27 (2006), pp. 1141-1167.
4. R. B. PEMBER, J. B. BELL, P. COLLELLA, W. Y. CRUTCHFIELD, AND M. WELCOME, An adaptive Cartesian grid method for unsteady compressible flow in irregular regions, J. Comput. Phys., 120 (1995), pp. 278-304.
5. M. J. BERGER, C. HELZEL, AND R. J. LEVEQUE, h-Box methods for the approximation of hyperbolic conservation laws on irregular grids, SIAM J. Numer. Anal., 41 (2003), pp. 893-918.
6. A. DITKOWSKI, K. DRIDI, AND J. S. HESTHAVEN, Convergent Cartesian grid methods for Maxwell's equations in complex geometries, J. Comput. Phys., 170 (2001), pp. 39-80.
7. B. GUSTAFSSON, H.-O. KREISS, AND J. OLIGER, Time Dependent Problems and Difference Methods, Wiley-Interscience, New York, 1995.
8. G. BROWNING, H-.O. KREISS, AND J. OLIGER, Mesh refinement, Math. Comp., 27 (1973), pp. 29-39.
9. D. L. BROWN, A note on the numerical solution of the wave equation with piecewise smooth coefficients, Math. Comput., 42 (1984), pp. 369-391.
10. A. N. TIKHONOV AND A. A. SAMARSKIǏ, Homogeneous difference schemes, Zh. Vychisl. Mat. i Mat. Fiz., 1 (1961), pp. 5-63.
11. C. ZHANG AND R. LEVEQUE, The immersed interface method for acoustic wave equations with discontinuous coefficients, Wave Motion, 25 (1997), pp. 237-263.
12. J. S. HESTHAVEN, High-order accurate methods in time-domain computational electromagnetics, Advances in Imaging and Electron Physics, 127 (2003), pp. 59-123.
13. S. ZHAO AND G. W. WEI, High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces, J. Comput. Phys., 200 (2004), pp. 60-103.
14. A. YEFET AND E. TURKEL, Fourth order compact implicit method for the Maxwell equations with discontinuous coefficients, Appl. Numer. Math., 33 (2000), pp. 125-134.
15. A. YEFET AND P. G. PETROPOULOS, A staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations, J. Comput. Phys., 168 (2001), pp. 286-315.
16. Z. XIE, C.-H. CHAN, AND B. ZHANG, An explicit fourth-order staggered finite-difference time-domain method for Maxwell's equations, J. Comput. Appl. Math., 147 (2002), pp. 75-98.
17. E. TURKEL AND A. YEFET, On the construction of a high order difference scheme for complex domains in a Cartesian grid, Appl. Numer. Math., 33 (2000), pp. 113-124.
18. W. CAI AND S. Z. DENG, An upwinding embedded boundary method for Maxwell's equations in media with material interfaces: 2D case, J. Comput. Phys., 190 (2003), pp. 159-183.
19. Z. XIE, C.-H. CHAN, AND B. ZHANG, An explicit fourth-order curvilinear staggered-grid FDTD method for Maxwell's equations, J. Comput. Phys., 175 (2002), pp. 739-763.
20. T. A. DRISCOLL AND B. FORNBERG, Block pseudospectral methods for Maxwell's equations II: Two-dimensional, discontinuous-coefficient case, SIAM J. Sci. Comput., 21 (1999), pp. 1146-1167.
21. R. WELLER AND G. H. SHORTLEY, Calculation of stresses within the boundary of photoelastic models, J. Appl. Mech., 6 (1939), pp. A71-A78.
22. H. JOHANSEN AND P. COLELLA, A Cartesian grid embedded boundary method for Poisson's equation on irregular domains, J. Comput. Phys., 147 (1998), pp. 60-85.
23. P. A. BERTHELSEN, A decomposed immersed interface method for variable coefficient elliptic equations with nonsmooth and discontinuous solutions, J. Comput. Phys., 197 (2004), pp. 364-386.
24. A. L. FOGELSON AND J. P. KEENER, Immersed interface methods for Neumann and related problems in two and three dimensions, SIAM J. Sci. Comput., 22 (2000), pp. 1630-1654.
25. Z. LI AND K. ITO, Maximum principle preserving schemes for interface problems with discontinuous coefficients, SIAM J. Sci. Comput., 23 (2001), pp. 339-361.
26. A. WIEGMANN AND K. P. BUBE, The immersed interface method for nonlinear differential equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal., 35 (1998), pp. 177-200.
27. G. MIE, Beiträge zur optik trüber medien, speziell kolloidaler metallösungen, Annalen der Physik, 25 (1908), pp. 377-445.
28. C. A. BALANIS, Advanced Engineering Electromagnetics, Wiley, New York, 1989.