Making simulations with the MNPBEM toolbox big: Hierarchical matrices and iterative solvers

MNPBEM is a Matlab toolbox for the simulation of metallic nanoparticles using a boundary element method (BEM) approach (Hohenester and Trügler, 2012), which is currently used by many research groups in the field of plasmonics. In this paper we introduce an extension for more efficient and faster simulations of large nanoparticles with several thousand to ten thousand boundary elements. Our approach is based on hierarchical matrices, for matrix compression and faster matrix manipulations, as well as iterative solvers for the BEM working equations. We discuss implementation details and present results for a few selected plasmonics applications.

MNPBEM是一款基于边界元法（boundary element method, BEM）的金属纳米粒子仿真Matlab工具箱（Hohenester与Trügler，2012），目前已被等离子体学领域的诸多研究团队广泛采用。本文针对包含数千至数万个边界元的大型纳米粒子，提出了一种可实现更高效、更快仿真的扩展方案。该方案基于用于矩阵压缩与快速矩阵操作的分层矩阵（hierarchical matrices），以及适配边界元法工作方程的迭代求解器。本文详细阐述了其实现细节，并展示了若干精选等离子体学应用的仿真结果。