Simulation of a microwave breakdown in air under atmospheric pressure is then performed and results are discussed. A numerical analysis shows its accuracy and computational efficiency on nested Cartesian grids. This numerical approach provides the Yee scheme with an efficient local-grid refinement capacity while preserving its stability. The patch of finite elements is used to calculate in an iterative manner the solution in the plasma region where a better precision is required. In this paper, the time-domain Maxwell's equations, which are coupled with the plasma transport equations via the time-varying electron current density, are solved with a two-level Schwarz type algorithm based on a variational formulation of the standard Yee scheme. The method uses the idea of finite element patch and can deal with very disparate length scales of the plasma. We consider the development of an efficient numerical method for the simulation of microwave discharge plasmas. 2LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France.1ONERA/DTIS, Université de Toulouse, Toulouse, France. Emanuele Arcese 1,2 *, François Rogier 1 and Jean-Pierre Boeuf 2
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