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Discretization of Poisson’s equation in two domains with non algebraic interface conditions for plasma simulations

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  • Villa, Andrea
  • Barbieri, Luca
  • Malgesini, Roberto
  • Buccella, Giacomo

Abstract

In this work, we treat the discretization of Poisson’s equation in two domains where interface conditions cannot be expressed by simple algebraic equations since they also contain differential terms. In particular, the more general and physical framework regards the solution of electrodynamic problems where surface conduction phenomena are taken into account. This kind of problems include, just to name a few, the interaction of plasma with solid dielectrics, or semi-conductive surfaces, the motion of charged ions in electro-active polymers and the interaction of charged fluids with porous matrices. In this work, we will identify a representative Poisson’s problem with non-algebraic interface conditions and we will study several discrete approaches to solve it. For each approach, we study the resolvability of the associated algebraic problem and we test its performances using some numerical tests.

Suggested Citation

  • Villa, Andrea & Barbieri, Luca & Malgesini, Roberto & Buccella, Giacomo, 2021. "Discretization of Poisson’s equation in two domains with non algebraic interface conditions for plasma simulations," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    • Handle: RePEc:eee:apmaco:v:403:y:2021:i:c:s0096300321002691
    DOI: 10.1016/j.amc.2021.126179
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    1. Villa, Andrea & Barbieri, Luca & Malgesini, Roberto, 2020. "Three dimensional simulation of the dynamics of electro active polymers using shell elements," Applied Mathematics and Computation, Elsevier, vol. 377(C).
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