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Introduction

We propose a new scheme for the finite-difference discretization of the wave equation. The development of this new scheme has been motivated by our needs for a well defined and accurate scheme of adaptive spatial mesh refinement in multidimensional electromagnetic Particle-In-Cell simulation.

The new scheme is obtained by the finite-difference discretization of a redundant form of the wave equation. The redundancy offers at the discrete level some freedom on the control numerical corrections by tuning additional free parameters with, for example, some application to noise reduction for shock propagation and reduction of the numerical Cerenkov instability. Another benefit of these additional parameters is the access to a mesh refinement algorithm using the `Transmitted-wave' boundary condition (that we developed first and motivated the new scheme).

This new scheme can be seen as an extension of the usual FDTD scheme (Yee scheme), to which it reduces for some specific values of the free parameters. For other values of the additional parameters, it reduces to other algorithms as, for example, the first or second order approximation of the Engquist and Majda outgoing-wave boundary condition, the Berenger Perfectly Matched Layer boundary condition or the `transmitted-wave' boundary condition for mesh refinement.



Jean-luc Vay
Tue Jan 13 15:57:00 PST 1998