Numerical methods for solving the 3D Neumann problem of laser‐induced plasma evolution in a semiconductor: Direct and iteration methods. Issue 3 (12th May 2020)

• Record Type: Journal Article
• Authors: Trofimov, Vyacheslav; Loginova, Maria; Egorenkov, Vladimir
• Is Part Of: Computational and mathematical methods. Volume 3:Issue 3(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-05-12
• Subjects: conservatism property -- contrast spatial structure -- femtosecond laser pulse -- finite‐difference scheme -- Neumann problem solvability -- numerical method -- optical bistability; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1092
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract: The article is devoted to an effective numerical method for solving the 3D problem of laser‐induced plasma evolution in a semiconductor. The physical processes under consideration are accompanied by the existence of the nonlinear feedback between semiconductor characteristics. Mathematically the problem is described by the set of time‐dependent nonlinear PDEs, which involves the Poisson equation with Neumann boundary conditions. One of the problem complexities correlates with providing of well‐known solvability condition for the Neumann problem at its numerical solution. This condition for the problem under consideration coincides with the fulfillment of the charge conservation law, and it is necessary to take into account at developing the numerical method. We apply and compare two numerical approaches: the direct method and the iteration method for a numerical solution of the Poisson equation together with the solution of other PDEs. The computer simulation results are shown that using the direct method leads to the solution distortion because of the presence of the problem nonlinear feedback between functions containing in the equations, and this feedback leads to the conservation law violation. Opposite, using the iteration method for the Poisson equation solution allows us to fulfill the conservation law of the equations set, whose numerical solution is based on developed iteration process.