A simplified implicit maxwell solver

  • Authors:

  • Paolo Ricci;Giovanni Lapenta;J. U. Brackbill

  • Affiliations:

  • Dipartimento di Fisica, Istituto Nazionale Fisica della Materia (INFM), Corso Duca degli Abruzzi 24, 10129 Torino, Italy and Dipartimento di Energetica, Politecnico di Torino, Corso Duca degli Abr ...;Dipartimento di Fisica, Istituto Nazionale Fisica della Materia (INFM), Corso Duca degli Abruzzi 24, 10129 Torino, Italy and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New M ...;Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2002

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Abstract

We apply the second-order formulation of Maxwell's equations proposed by Jiang et al. (1996, J. Comput. Phys. 125, 104) to the solution of the implicit formulation of the three-dimensional, time-dependent Vlasov-Maxwell's system. An implicit finite difference algorithm is developed to solve the Maxwell's equations in a bounded domain with physical boundary conditions comprising electrically conducting walls (perfect conductors) and constant magnetic flux walls. We formulate the boundary conditions for Maxwell's equations to satisfy Poisson's equation throughout the domain by solving it only on the boundary. This eliminates the need for a separate projection step. We compare numerical results with analytical solutions for electro-magnetic waves in vacuo, and using the implicit particle-in-cell code CELESTE3D, we test the new solver on the geospace environment modeling magnetic reconnection challenge problem.