A simplified implicit Maxwell solver

Journal of Computational Physics

Volumn 183, Issue 1, 2002, Pages 117-141

  Ricci, Paolo ^a,b   Lapenta, Giovanni ^a,c   Brackbill, J U ^c  

^a INFM   (Italy)

^b POLITECNICO DI TORINO   (Italy)

^c LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Boundary conditions; Divergence constraints; Implicit numerical method; Maxwell's equations; Particle in cell implicit method

Indexed keywords

BOUNDARY CONDITIONS; DOMAIN WALLS; ELECTROMAGNETIC WAVES; EQUATIONS OF MOTION; NUMERICAL METHODS; POISSON EQUATION; VLASOV EQUATION;

DIVERGENCE CONSTRAINT; FINITE-DIFFERENCE ALGORITHMS; IMPLICIT FORMULATION; IMPLICIT METHODS; IMPLICIT NUMERICAL METHOD; PARTICLE IN CELL; PARTICLE-IN-CELL IMPLICIT METHOD; SECOND ORDERS; TIME DEPENDENT; VLASOV-MAXWELL SYSTEM;

MAXWELL EQUATIONS;

EID: 0037146425     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2002.7170     Document Type: Article

References (62)

1. F. Assous, P. Degond, E. Heintze, P. A. Raviart, and J. Segre, On a finite-element method for solving the 3-dimensional Maxwell equations, J. Comput. Phys. 109, 222 (1993).
2. F. Assous, P. Ciarlet, and E. Sonnendrücker, Resolution of the Maxwell equations in a domain with reentrant corners, Model. Math. Anal. Numer 32, 359 (1998).
3. D. C. Barnes, T. Kamimura, J.-N. Leboeuf, and T. Tajima, Implicit particle simulation of magnetized plasmas, J. Comput. Phys. 52, 480 (1983).
4. P. A. Bernhardt and J. U. Brackbill, Solution of elliptic equations using fast Poisson solvers, J. Comput. Phys. 53, 382 (1984).
5. T. S. Bird, Propagation and radiation of characteristics of rib waveguide, Electron. Lett. 13, 401 (1997).
6. C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, New York, 1985).
7. J. Birn, J. F. Drake, M. A. Shay, B. N. Rogers, R. E. Denton, M. Hesse, M. Kuznetsova, A. W. Ma, A. Bhattacharjee, A. Otto, and P. L. Pritchett, Geospace Environment Modeling (GEM) magnetic reconnection challenge, J. Geophys. Res. 106, 3715 (2001).
8. D. Biskamp, E. Schwartz, and J. F. Drake, Two fluid theory of collisionless magnetic reconnection, Phys. Plasmas 4, 1002 (1997).
9. J. U. Brackbill and D. W. Forslund, An implicit method for electromagnetic plasma simulation in two dimensions, J. Comput. Phys. 46, 271 (1982).
10. J. U. Brackbill, D. W. Forslund, K. B. Quest, and D. Winske, Nonlinear evolution to the lower-hybrid drift instability, Phys. Fluids 27, 2682 (1984).
11. J. U. Brackbill and D. W. Forslund, Simulation of low-frequency electromagnetic phenomena in plasmas, in Multiple Time Scales, edited by J. U. Brackbill and B. I. Cohen (Academic Press, San Diego, 1985), p. 271.
12. A. B. Langdon and D. C. Barnes, Direct implicit plasma simulation, in Multiple Time Scales, edited by J. U. Brackbill and B. I. Cohen (Academic Press, San Diego, 1985), p. 271.
13. J. U. Brackbill and H. X. Vu, Electron kinetic effects in switch-off slow shocks, Geophys. Res. Lett. 20, 2015 (1993).
14. B. I. Cohen, A. B. Langdon, D. W. Hewett, and R, J. Pocassini, Performance and optimization of direct implicit particle simulation, J. Comput. Phys. 81, 151 (1989).
15. B. I. Cohen, A. B. Langdon, and A. Friedman, Implicit time integration for plasma simulation, J. Comput. Phys. 46, 15 (1982).
16. pe Δt ≫ 1, J. Comput. Phys. 42, 337 (1981).
17. J. Dreher, U. Arendt, and K. Schindler, Particle simulations of collisionless reconnection in magnetotail configuration including electron dynamics, J. Geophys. Res. 101, 27375 (1996).
18. T. Zh. Esirkepov, Exact charge conservation scheme for particle-in-cell simulation with an arbitrary form-factor, Comput. Phys. Commun. 135, 144 (2001).
19. D. W. Forslund and J. U. Brackbill, Magnetic-field induced surface transport on laser-irradiated foils, Phys. Rev. Lett. 48, 1614 (1982).
20. D. W. Forslund, K. B. Quest, J. U. Brackbill, and K. Lee, Collisionless dissipation in quasi-perpendicular shocks, J. Geophys. Res. 89, 2142 (1984).
21. M. Hesse, J. Birn, and M. M. Kuznetsova, Collisionless magnetic reconnection: Electron processes and transport modelling, J. Geophys. Res. 106, 3721 (2001).
22. D. W. Hewett and A. B. Langdon, Electromagnetic direct implicit plasma simulation, J. Comput. Phys. 72, 121 (1987).
23. D. W. Hewett, G. E. Frances, and C. E. Max, New regimes of magnetic reconnection in collisionless plasmas, Phys. Rev. Lett. 61, 893 (1988).
24. P. Hillion, Beware of Maxwell's divergence equations, J. Comput. Phys. 132, 154 (1997).
25. R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles (Adam Hilger, Bristol and Philadelphia, 1988).
26. R. Horiuchi and T. Sato, Three-dimensional particle simulation of plasma instabilities and collisionless reconnection in a current sheet, Phys. Plasmas 6, 4565 (1999).
27. T. Kamimura, E. Montalvo, D. C. Barnes, J. N. Leboeuf, and T. Tajima, Implicit particle simulation of electromagnetic plasma phenomena, J. Comput. Phys. 100, 77 (1992).
28. U. Kangro and R. Nicolaides, Divergence boundary conditions for vector Helmholtz equations with divergence constraints, Model. Math. Anal. Numer. 33, 479 (1999).
29. D. A. Kpoll, G. Lapenta, and J. U. Brackbill, A multilevel iterative field solver for implicit, kinetic, plasma simulation, J. Comput. Phys. 149, 377 (1999).
30. W. L. Kruer, The Physics of Laser Plasma Interactions (Addison-Wesley, Redwood City, CA, 1988).
31. M. M. Kuznetsova, M. Hesse, and D. Winske, Collisionless reconnection supported by nongyrotropic pressure effects in hybrid and particle simulations, J. Geophys. Res. 106, 3799 (2001).
32. B.-N. Jiang, J. Wu, and L. A. Povinelli, The origin of spurious solutions in computational electromagnetics, J. Comput. Phys. 125, 104 (1996).
33. A. B. Langdon and B. F. Lasinski, Electromagnetic and relativistic plasma simulation methods, in Methods in Computational Physics, edited by J. Killeen (Academic Press, New York, 1976), p. 327.
34. A. B. Langdon, B. I. Cohen, and A. Friedman, Direct implicit large time-step particle simulation of plasmas, J. Comput. Phys. 51, 107 (1983).
35. G. Lapenta and J. U. Brackbill, Contact discontinuities in collisionless plasmas: A comparison of hybrid and kinetic simulations, Geophys. Res. Lett. 23, 1713 (1996).
36. G. Lapenta and J. U. Brackbill, Implicit Adaptive Grid Plasma Simulation, 5th Int. School/Symposium for Space Simulation, Kyoto, Japan (March 13-19, 1997).
37. G. Lapenta and J. U. Brackbill, 3D reconnection due to oblique modes: A simulation of Harris current sheet, Nonlinear Proc. Geophys. 7, 151 (2000).
38. Deleted in proof.
39. B. Lembege and F. Simonet, Hybrid and particle simulations of an interface expansion and of collisionless shock: A comparative and qualitative study, Phys. Plasmas 8, 3967 (2001).
40. I. D. Mayergoyz and J. D'Angelo, A new point of view on the mathematical structure of Maxwell's equations, IEEE Trans. Magnetics 29, 1315 (1993).
41. R. J. Mason, Implicit moment particle simulation of plasmas, J. Comput. Phys. 41, 233 (1981).
42. R. J. Mason, An electromagnetic field algorithm for 2D implicit plasma simulation, J. Comput. Phys. 71, 429 (1987).
43. R. J. Mason, P. L. Auer, R. N. Sudan, B. V. Olivier, C. E. Seyler, and J. B. Greenly, Nonlinear magnetic field transport in opening switch plasmas, Phys. Fluids B 5, 1115 (1993).
44. M. Oieroset, T. D. Phan, M. Fujimoto, R. P. Lin, and R. P. Lepping, In situ detection of collisionless reconnection in the Earth's magnetotail, Nature 412, 414 (2001).
45. P. L. Pritchett, Geospace Environment Modeling magnetic reconnection challenge: Simulation with a full particle electromagnetic code, J. Geophys. Res. 106, 3783 (2001).
46. K. B. Quest, D. W. Forslund, J. U. Brackbill, and K. Lee, Collisionless dissipation processes in quasi-parallel shocks, Geophys. Res. Lett. 10, 471 (1983).
47. P. W. Rambo, J. Ambrosiano, A. Friednam, and D. E. Nielsen, Jr., Temporal and spatial filtering remedies for dispertion in electromagnetic particle codes, in Proc. l3th Conference on the Numerical Simulation of Plasmas, Santa Fe, New Mexico (September 17-20, 1989). [Paper PMA 9]
48. Y. Saad and M. H. Schultz, GMRES: A Generalised Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM J. Sci. Stat. Comput. 7, 856 (1986).
49. E. Schwieg and W. B. Bridges, Computer analysis of dielectric waveguide: A finite-difference method, IEEE Trans. Microwave Theory Technol. 32, 531 (1984).
50. J. S. Shang and D. Gaitonde, Characteristic-based, time-dependent Maxwell equation solvers on a general curvilinear frame, AIAA J. 33, 491 (1995).
51. M. A. Shay, J. F. Drake, B. N. Rogers, and R. E. Denton, Alfvenic collisionless magnetic reconnection and the Hall term, J. Geophys. Res. 106, 3759 (2001).
52. H. Shimazu, S. Machida, and M. Tanaka, Macroparticle simulation of collisionless parallel shocks generated by solar wind and planetary plasma interactions, J. Geophys. Res. 101, 7647 (1997).
53. C. C. Su, Origin of spurious modes in the analysis of optical fiber using the finite-element or finite-difference technique, Electron. Lett. 21, 858 (1985).
54. D. Sulsky and J. U. Brackbill, A numerical method for suspension flow, J. Comput. Phys. 96, 339 (1991).
55. T. Tajima, Computational Plasma Physics: With Applications to Fusion and Astrophysics (Addison-Wesley, Redwood City, CA, 1989).
56. M. Tanaka, Macroscale implicit electromagnetic particle simulation of magnetized plasmas, J. Comput. Phys. 79, 209 (1988).
57. M. Tanaka, The Macro-EM particle simulation method and a study of collisionless reconnection, J. Comput. Phys. 87, 117 (1995).
58. J. Villasenor and O. Buneman, Rigorous charge conservation for local electromagnetic field solvers, Comput. Phys. Commun. 69, 306 (1992).
59. H. X. Vu and J. U. Brackbill, CELEST1D: An implicit, fully kinetic model for low-frequency, electromagnetic plasma simulation, Comput. Phys. Commun. 69, 253 (1992).
60. J. R. Winkler and J. B. Davies, Elimination of spurious modes in finite-element analysis, J. Comput. Phys. 56, 1 (1984).
61. D. Winske and N. Omidi, A nonspecialist's guide to kinetic simulations of space plasmas, J. Geophys. Res. 101, 17287 (1996).
62. M. A. Yates, D. B. VanHulsteyn. H. Rutkowski, G. Kyrala, and J. U. Brackbill, Experimental evidence for self-generated magnetic fields and remote energy deposition in laser-irradiated targets, Phys. Rev. Lett. 49, 1702 (1982).