Implicit scheme for Maxwell equations solution in case of flat 3D domains

International Conference on Computer Simulation in Physics and Beyond 2015

物理学;计算机科学

Boronina, Marina^1 ; Vshivkov, Vitaly^1

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, Russia^1

关键词: Approximation orders;    Conditional stability;    Electric and magnetic fields;    Equations solution;    Finite difference scheme;    Propagation speed;    Stability condition;    Three-dimensional domain;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/681/1/012032/pdf
DOI  :  10.1088/1742-6596/681/1/012032

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

We present a new finite-difference scheme for Maxwell's equations solution for three-dimensional domains with different scales in different directions. The stability condition of the standard leap-frog scheme requires decreasing of the time-step with decreasing of the minimal spatial step, which depends on the minimal domain size. We overcome the conditional stability by modifying the standard scheme adding implicitness in the direction of the smallest size. The new scheme satisfies the Gauss law for the electric and magnetic fields in the final- differences. The approximation order, the maintenance of the wave amplitude and propagation speed, the invariance of the wave propagation on angle with the coordinate axes are analyzed.