Block pseudospectral methods for Maxwell's equations II: two-dimensional, discontinuous-coefficient case

SIAM Journal of Scientific Computing

Volumn 21, Issue 3, 1999, Pages 1146-1167

  Driscoll, Tobin A ^a   Fornberg, Bengt ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; ONE DIMENSIONAL; PROBLEM SOLVING; TWO DIMENSIONAL;

BLOCK PSEUDO SPECTRAL METHODS; COMPOSITE GRIDS;

MAXWELL EQUATIONS;

EID: 0033293698     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S106482759833320X     Document Type: Article

References (27)

1. S. ABARBANEL AND D. GOTTLIEB, A mathematical analysis of the PML method, J. Comput. Phys., 134 (1997), pp. 357-363.
2. S. ABARBANEL AND D. GOTTLIEB, On the construction and analysis of absorbing layers in CEM, Appl. Numer. Math., 27 (1998), pp. 331-340.
3. 1 conforming finite element method, J. Comput. Phys., 128 (1996), pp. 363-380.
4. A. BAMBERGER, R. GLOWINSKI, AND Q. H. TRAN, A domain decomposition method for the acoustic wave equation with discontinuous coefficients and grid change, SIAM J. Numer. Anal., 34 (1997), pp. 603-639.
5. J.-P. BERENGER, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114 (1994), pp. 185-200.
6. M. BJØRHUS, The ODE formulation of hyperbolic PDEs discretized by the spectral collocation method, SIAM J. Sci. Comput., 16 (1995), pp. 542-557.
7. M. H. CARPENTER, D. GOTTLIEB, S. ABARBANEL, AND W. S. DON, The theoretical accuracy of Runge-Kutta time discretizations for the initial-boundary value problem: A study of the boundary error, SIAM J. Sci. Comput., 16 (1995), pp. 1241-1252.
8. G. CHESSHIRE AND W. D. HENSHAW, Composite overlapping meshes for the solution of partial differential equations, J. Comput. Phys., 90 (1990), pp. 1-64.
9. T. A. DRISCOLL AND B. FORNBERG, A block pseudospectral method for Maxwell's equations: I. One-dimensional case, J. Comput. Phys., 140 (1998), pp. 1-19.
10. E. FACCIOLI, A. QUARTERONI, AND A. TAGLIANI, Spectral multidomain methods for the simulation of wave propagation in heterogeneous media, in Domain Decomposition Methods in Science and Engineering, Sixth International Conference on Domain Decomposition, Como, Italy, A. Quarteroni, J. Periaux, Y. A. Kuznetsov, and O. B. Widlund, eds., Contemporary Math. 157, AMS, Providence, RI, 1994, pp. 447-455.
11. B. FORNBERG, High-order finite differences and the pseudospectral method on staggered grids, SIAM J. Numer. Anal., 27 (1990), pp. 904-918.
12. B. FORNBERG, A Practical Guide to Pseudospectral Methods, Cambridge University Press, Cambridge, UK, 1996.
13. B. FORNBERG AND M. CHRIST, Spatial finite difference approximations for wave-type equations, SIAM J. Numer. Anal., to appear.
14. P. HANLEY, A strategy for the efficient simulation of viscous compressible flows using a multidomain pseudospectral approach, J. Comput. Phys., 108 (1993), pp. 153-158.
15. D. A. KOPRIVA, Computation of hyperbolic equations on complicated domains with patched and overset Chebyshev grids, SIAM J. Sci. Statist. Comput., 10 (1989), pp. 120-132.
16. D. A. KOPRIVA, A conservative staggered-grid Chebyshev multidomain method for compressible flows. II. A semi-structured method, J. Comput. Phys., 128 (1996), pp. 475-488.
17. D. A. KOPRIVA AND J. H. KOLIAS, A conservative staggered-grid Chebyshev multidomain method for compressible flows, J. Comput. Phys., 125 (1996), pp. 244-261.
18. I. LIE, Interface conditions for heterogeneous domain decomposition: Coupling of different hyperbolic systems, in Domain Decomposition Methods in Science and Engineering: Sixth International Conference on Domain Decomposition, Como, Italy, A. Quarteroni, J. Periaux, Y. A. Kuznetsov, and O. B. Widlund, eds., Contemporary Math. 157, AMS, Providence, RI, 1994, pp. 469-476.
19. I. LIE, Multidomain solution of advection problems by Chebyshev spectral collocation, SIAM J. Sci. Comput., 9 (1994), pp. 39-64.
20. E. LUO AND H.-O. KREISS, Pseudospectral vs. finite difference methods for initial value problems with discontinuous coefficient, SIAM J. Sci. Comput., 20 (1998), pp. 148-163.
21. D. PATHRIA, The correct formulation of intermediate boundary conditions for Runge-Kutta time integration of initial-boundary value problems, SIAM J. Sci. Comput., 18 (1997), pp. 1255-1266.
22. A. QUARTERONI, Domain decomposition methods for systems of conservation laws: Spectral collocation approximations, SIAM J. Sci. Statist. Comput., 11 (1990), pp. 1029-1052.
23. J. R. REITZ, F. J. MILFORD, AND R. W. CHRISTY, Foundations of Electromagnetic Theory, Addison-Wesley, Reading, MA, 1979.
24. A. TAFLOVE, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House, Boston, 1995.
25. B. YANG, D. GOTTLIEB, AND J. S. HESTHAVEN, Spectral simulations of electromagnetic wave scattering, J. Comput., Phys., 137 (1997), pp. 1-15.
26. K. S. YEE, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. Antennas Prop., 14 (1966), pp. 302-307.
27. R. W. ZIOLKOWSKI, Time-derivative Lorentz material model-based absorbing boundary condition, IEEE Trans. Antennas Prop., 45 (1997), pp. 1530-1535.