Multigrid preconditioning for Krylov methods for time-harmonic Maxwell's equations in three dimensions

SIAM Journal on Scientific Computing

Volumn 24, Issue 2, 2003, Pages 702-718

  Aruliah, D A ^a   Ascher, U M ^b  

^a FIELDS INSTITUTE   (Canada)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Finite volume; Krylov methods; Maxwell's equations; Multigrid preconditioning; Solution discontinuities

Indexed keywords

FINITE VOLUME METHOD; MATHEMATICAL MODELS; MAXWELL EQUATIONS; PROBLEM SOLVING; VECTORS;

MULTIGRID PRECONDITIONING;

ELECTROMAGNETIC WAVES;

EID: 0037249731     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827501387358     Document Type: Article

References (31)

1. R. E. ALCOUFFE, A. BRANDT, J. E. DENDY, JR., AND J. W. PAINTER, The multi-grid methods for the diffusion equation with strongly discontinuous coefficients, SIAM J. Sci. Statist. Comput., 2 (1981), pp. 430-454.
2. D. ARULIAH, Fast Solver for Time-Harmonic Maxwell's Equations in 3D, Ph.D. thesis, Department of Computer Science, University of British Columbia, Vancouver, BC, Canada, 2001.
3. D. ARULIAH, U. ASCHER, E. HABER, AND D. OLDENBURG, A method for the forward modelling of 3D electromagnetic quasi-static problems, Math. Models Methods Appl. Sci., 11 (2001), pp. 1-21.
4. R. BARRETT, M. BERRY, T. F. CHAN, J. DEMMEL, J. DONATO, J. DONGARRA, V. EIJKHOUT, R. POZO, C. ROMINE, AND H. VAN DER VORST, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, 1994.
5. R. BECK, Algebraic Multigrid by Component Splitting for Edge Elements on Simplicial Triangulations, Tech. Report, SC 99-40 Konrad-Zuse-Zentrum, Berlin, Germany, 1999. Available online at http://www.zib.de/bib/pub/pw/index.en.html
6. R. BECK, P. DEUFLHARD, R. HIPTMAIR, R. HOPPE, AND B. WOHLMUTH, Adaptive multilevel methods for edge element discretizations of Maxwell's equations, Surveys Math. Indust., 8 (1999), pp. 271-312.
7. A. BOSSAVIT, Computational Electromagnetism. Variational Formulation, Complementarity, Edge Elements, Academic Press, New York, 1998.
8. A. BRANDT, Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, The Weizmann Institute of Science, Rehovot, Israel, 1984.
9. T. P. CHAN AND H. C. ELMAN, Fourier analysis of iterative methods for elliptic boundary value problems, SIAM Rev., 31 (1989), pp. 20-49.
10. J. W. DEMMEL, Applied Numerical Linear Algebra, SIAM, Philadelphia, 1997.
11. J. E. DENDY, JR., Two multigrid methods for three-dimensional problems with discontinuous and anisotropic coefficients, SIAM J. Sci. Statist. Comput., 8 (1987), pp. 673-685.
12. J. E. DENDY, Black box multigrid, J. Comput. Phys., 48 (1982), pp. 366-386.
13. H. C. ELMAN, Preconditioning for the steady-state Navier-Stokes equations with low viscosity, SIAM J. Sci. Comput., 20 (1999), pp. 1299-1316.
14. M. EVERETT AND A. SCHULTZ, Geomagnetic induction in a heterogenous sphere: Azimuthally symmetric test computations and the response of an undulating 660-km discontinuity, J. Geophys. Res., 101 (1996), pp. 2765-2783.
15. J. GOPALAKRISHNAN AND J. PASCIAK, Overlapping Schwarz preconditioned for indefinite Maxwell equations, Math. Comp., to appear.
16. E. HABER AND U. ASCHER, Fast finite volume simulation of 3D electromagnetic problems with highly discontinuous coefficients, SIAM J. Sci. Comput., 22 (2001), pp. 1943-1961.
17. E. HABER, U. ASCHER, D. ARULIAH, AND D. OLDENBURG, Fast simulation of 3D electromagnetic using potentials, J. Comput. Phys., 163 (2000), pp. 150-171.
18. W. HACKBUSCH, Multi-Grid Methods and Applications, Springer-Verlag, New York, 1985.
19. R. HIPTMAIR, Multigrid method for Maxwell's equations, SIAM J. Numer. Anal., 36 (1998), pp. 204-225.
20. J. JIN, The Finite Element Method in Electromagnetics, John Wiley, New York, 1993.
21. C. MATTIUSSI, An analysis of finite volume, finite element, and finite difference methods using some concepts from algebraic topology, J. Comput. Phys., 133 (1997), pp. 289-309.
22. J. D. MOULTON, Numerical Implementation of Nodal Methods, Ph.D. thesis, Institute of Applied Mathematics, University of British Columbia, Vancouver, BC, Canada, 1996.
23. G. NEWMAN AND D. ALUMBAUGH, Frequency-domain modelling of airborne electromagnetic responses using staggered finite differences, Geophys. Prospecting, 43 (1995), pp. 1021-1042.
24. I. PERUGIA, V. SIMONCINI, AND M. ARIOLI, Linear algebra methods in a mixed approximation of magnetostatic problems, SIAM J. Sci. Comput., 21 (1999), pp. 1085-1101.
25. R. RICHTMYER AND K. MORTON, Difference Methods for Initial-Value Problems, John Wiley, New York, 1967.
26. Y. SAAD, Iterative Methods for Sparse Linear Systems, PWS Publishing Company, Boston, MA, 1996.
27. S. SELBERHERR, Analysis and Simulation of Semiconductor Devices, Springer-Verlag, Vienna, 1984.
28. A. TAFLOVE, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House Publishers, Norwood, MA, 1995.
29. J.T. WEAVER, Mathematical Methods for Geo-Electromagnetic Induction, John Wiley, New York, 1994.
30. P. WESSELING, An Introduction to Multigrid Methods, John Wiley, Chichester, 1992.
31. D. ZWILLINGER, ED., Standard Mathematical Tables and Formulae, CRC Press, Boca Raton, FL, 1996.