Solving Vlasov-Maxwell equations in singular geometries

Authors:
Franck Assous;Patrick Ciarlet, Jr.
Affiliations:
Ariel University Center, Ariel, Israel and Bar-Ilan University, 52900 Ramat-Gan, Israel;Bar-Ilan University, 52900 Ramat-Gan, Israel and ENSTA,32 bvd Victor, 75739, Paris Cedex 15, France
Venue:
Mathematics and Computers in Simulation
Year:
2008

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Abstract

This paper is devoted to the solution of the time-dependent Vlasov-Maxwell equations in singular geometries, i.e. when the boundary includes reentrant corners or edges. Indeed, computing the electromagnetic fields in this case is a challenge per se, as these geometrical singularities generate very strong solutions in their neighborhood. Moreover, they have also an influence over the solution of the Vlasov equation, through the coupling. We propose here a method to solve this problem, illustrated by numerical examples.