Application of the iterative approach to modal methods for the solution of Maxwell's equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:300

Article

Semenikhin, Igor^1,2  Zanuccoli, Mauro^3,4 

[1] Inst Phys & Technol RAS, Moscow 117218, Russia

[2] Tohoku Univ, Res Inst Elect Commun, Sendai, Miyagi 9808577, Japan

[3] ARCES DEIS Univ Bologna, I-47521 Cesena, FC, Italy

[4] IUNET, I-47521 Cesena, FC, Italy

关键词: Maxwell's equations;    Modal methods;    Computational complexity;    Iterative approach;    Scattering matrix;    Diffraction gratings;   

DOI  :  10.1016/j.jcp.2015.07.052

来源: Elsevier

【 摘 要 】

In this work we discuss the possibility to reduce the computational complexity of modal methods, i.e. methods based on eigenmodes expansion, from the third power to the second power of the number of eigenmodes by applying the iterative technique. The proposed approach is based on the calculation of the eigenmodes part by part by using shift-and-invert iterative procedure and by utilizing the iterative approach to solve linear equations to compute eigenmodes expansion coefficients. As practical implementation, the iterative modal methods based on polynomials and trigonometric functions as well as on finite-difference scheme are developed. Alternatives to the scattering matrix (S-matrix) technique which are based on pure iterative or mixed direct-iterative approaches allowing to markedly reduce the number of required numerical operations are discussed. Additionally, the possibility of diminishing the memory demand of the whole algorithm from second to first power of the number of modes by implementing the iterative approach is demonstrated. This allows to carry out calculations up to hundreds of thousands eigenmodes without using a supercomputer. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free