Three-dimensional finite-volume solver for the Maxwell equations with divergence cleaning on unstructured meshes

Computer Physics Communications

Volumn 130, Issue 1, 2000, Pages 83-117

  Munz, C D ^a   Ommes, P ^b   Schneider, R ^c  

^a UNIVERSITY OF STUTTGART   (Germany)

^b CEA SACLAY   (France)

^c KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; COMPUTER SOFTWARE; CONSTRAINT THEORY; FINITE VOLUME METHOD; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; MAXWELL EQUATIONS; PARALLEL PROCESSING SYSTEMS; TIME DOMAIN ANALYSIS;

MAXWELL-VLASOV EQUATIONS; PARTICLE-IN-CELL METHOD; POISSON EQUATION;

ELECTROMAGNETIC WAVE PROPAGATION;

EID: 0034228981     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0010-4655(00)00045-X     Document Type: Article

References (46)

1. F. Assous, P. Degond, E. Heintze, P. Raviart, J. Segré, On a finite-element method for solving the three-dimensional Maxwell equations, J. Comput. Phys. 109 (1993) 222-237.
2. 1 conforming finite element method, J. Comput. Phys. 126 (1996) 363-380.
3. C.K. Birdsall, A.B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, New York, 1985).
4. H.-J. Bluhm, P. Hoppé, H. Bachmann, W. Bauer, K. Baumung, L. Buth, J.B. Greenly, H.U. Karow, D. Rusch, E. Stein, O. Stoltz, Progress in the development of a high power focusing B-applied extractor type ion diode for the 1.5 TW pulse generator KALIF, in: Proc. 8th Int. Conf. on High-power Particle Beams, Novosibirsk (World Scientific, Singapore, 1990) pp. 451-456.
5. J.P. Boris, Relativistic plasma simulations - Optimization of a hybrid code, in: Proc. 4th Conf. Num. Sim. of Plasmas (NRL Washington, Washington, DC, 1970) pp. 3-67.
6. J.P. Cioni, L. Fezoui, H. Steve, A parallel time-domain Maxwell solver using upwind schemes and triangular meshes, IMPACT of Comput. Sci. and Eng. 5 (1993) 215-247.
7. E. Courant, E. Issacson, M. Rees, On the solution of nonlinear hyperbolic differential equations, Comm. Pure Appl. Math. 5 (1953) 243-255.
8. L. Durlofsky, B. Engquist, S. Osher, Triangle based adaptive stencils for the solution of hyperbolic conservation laws, J. Comput. Phys. 98 (1992) 64-73.
9. J.W Eastwood, The virtual particle electromagnetic particle-mesh method, Comput. Phys. Commun. 64 (1991) 252-266.
10. M. Fedoruk, C.-D. Munz, P. Omnes, R. Schneider, A Maxwell-Lorentz solver for self-consistent particle-field simulations on unstructured grids, Forschungszentrum Karlsruhe - Technik und Umwelt, FZKA 6115 (1998).
11. E. Godlewski, P.A. Raviart, Numerical approximation of hyperbolic systems of conservation laws, Applied Mathematic Sciences, Vol. 118 (Springer, New York, Heidelberg, Berlin, 1986).
12. R.W. Hockney, J.W. Eastwood, Computer Simulation Using Particles (McGraw-Hill, New York, 1981).
13. R. Holland, Finite-difference solution of Maxwell's equations in generalized nonorthogonal coordinates, IEEE Trans. Nucl. Sci. 30 (1983) 4589-4591.
14. J.M. Hyman, M.Y Shashkov, Natural discretizations for the divergence, gradient, and curl on logically rectangular grids, Comput. Math. Appl. 33 (1997) 81-104.
15. B. Jiang, J. Wu, L.A. Povinelli, The origin of spurious solutions in computational electromagnetics, J. Comput. Phys. 125 (1996) 104-123.
16. D. Kröner, Numerical Schemes for Conservation Laws (Wiley Teubner, Chichester, 1997).
17. A.B. Langdon, On enforcing Gauss' law in electromagnetic particle-in-cell codes, Comput. Phys. Commun. 70 (1992) 447-450.
18. B.V. Leer, Towards the ultimative conservative difference scheme V. A second order sequel to Godunov's method, J. Comput. Phys. 32 (1979) 101-136.
19. R.J. LeVeque, Numerical Methods for Conservation Laws (Birkhäuser, Basel, 1990).
20. N.K. Madsen, R.W. Ziolkowski, Numerical solution of the Maxwell's equations in the time domain using irregular nonorthogonal grids, Wave Motion 10 (1988) 583-596.
21. N.K. Madsen, R.W. Ziolkowski, A three-dimensional modified finite volume technique for Maxwell's equations, Electromagnetics 10 (1990) 147-161.
22. G. Marchuk, Methods of Numerical Mathematics (Springer-Verlag, New York, Heidelberg, Berlin, 1975).
23. B. Marder, A method incorporating Gauß' law into electromagnetic PIC codes, J. Comput. Phys. 68 (1987) 48-55.
24. V.S.A.H. Mohammadian, W. Hall, Computation of electromagnetic scattering and radiation using a time-domain finite-volume discretization procedure, Comput. Phys. Commun. 68 (1991) 175-196.
25. C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer, Berlin, 1969).
26. C.-D. Munz, P. Omnes, R. Schneider, E. Sonnendrücker, U. Voss, Divergence correction techniques for Maxwell solvers based on a hyperbolic model, J. Comput. Phys. (1999) to appear.
27. C.-D. Munz, R. Schneider, E. Sonnendrücker, E. Stein, U. Voss, T. Westermann, A finite-volume particle-in-cell method for the numerical treatment of the Maxwell-Lorentz equations on boundary-fitted meshes, Int. J. Numer. Meth. Engng. 44 (1999) 461-487.
28. C.-D. Munz, R. Schneider, E. Sonnendrücker, U. Voss, Maxwell's equations when the charge conservation is not satisfied, C. R. Acad. Sci. (CRAS) Paris 328 (1999) 431-436.
29. C.-D. Munz, R. Schneider, U. Voss, A finite-volume method for Maxwell equations in time domain, SIAM J. Sci. Comput. (1999) to appear.
30. G. Mur, Compatibility relations and the finite-element formulation of electromagnetic field problems, IEEE Trans. Magnetics 30 (1994) 2972-2975.
31. G. Mur, The fallacy of edge elements, IEEE Trans. Magnetics 34 (1998) 3244-3247.
32. G. Mur, A. de Hoop, A finite-element method for computing three-dimensional electromagnetic fields in inhomogeneous media, IEEE Trans. Magnetics 21 (1985) 2188-2191.
33. J. Nédélec, Mixed finite elements in R3, Numer. Math. 35 (1980) 315-341.
34. D. Nielsen, A. Drobot, An analysis of the pseudo-current method, J. Comput. Phys. 89 (1990) 31-40.
35. A.F. Peterson, Absorbing boundary conditions for the vector wave equation, Microwave and Opt. Techn. Lett. 1 (1988) 62-64.
36. D. Seidel, M. Kiefer, R. Coats, T. Pointon, J. Quintenz, W. Johnson, The 3D, electromagnetic, particle-in-cell code QUICKSILVER, in: Proc. Europhys. Conf. on Compt. Physics, Amsterdam, A. Tenner (Ed.) (World Scientific, Singapore, 1991) (1990).
37. J. Shang, A fractional-step method for solving 3D, time-domain Maxwell equations, J. Comput. Phys. 118 (1995) 109-119.
38. T. Sonar, Mehrdimensionale ENO-Verfahren, Teubner, Advances in Numerical Mathematics (Stuttgart, 1997).
39. G. Strang, On the construction and comparison of difference schemes, SIAM J. Num. Anal. 5 (1968) 505-517.
40. A. Taflove, Computational Electrodynamics: The Finite-difference Time-Domain Method (Artech House, Boston, 1995).
41. F.L. Teixeira, W.C. Chew, Lattice electromagnetic theory from a topological viewpoint, J. Math. Phys. 40 (1999) 169-187.
42. J.F. Thompson, Z.U.A. Warsi, C.W. Mastin, Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review, J. Comput. Phys. 47 (1982) 1.
43. J. Villasenor, O. Buneman, Rigorous charge conservation for local electromagnetic field solvers, Comput. Phys. Commun. 69 (1992) 306-316.
44. T. Weiland, Eine Methode zur Loesung der Maxwellschen Gleichungen fuer sechskomponentige Felder auf diskreter Basis, AEU Arch. Elektron. Uebertragungstech. Electron Commun. 14 (1977) 116-119.
45. T. Weiland, Time domain electromagnetic field computation with finite difference methods, Int. J. Numer. Model 9 (1996) 296-319.
46. K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. Ant. Prop. 14 (1966) 302-307.