Fast and accurate analysis of large-scale composite structures with the parallel multilevel fast multipole algorithm.
Fast and accurate analysis of large-scale composite structures with the parallel multilevel fast multipole algorithm.
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DOI：
10.1364/josaa.30.000509
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发表时间：
2013-03
期刊：
影响因子：
--
通讯作者：
Ö. Ergül;L. Gürel
中科院分区：
文献类型：
--
作者：
Ö. Ergül;L. Gürel
复杂光学结构的精确电磁建模提出了若干挑战。光学超材料和等离子体结构由多个共存的介电和/或导电部分组成。这种复合结构可以具有不同的电导率和介电常数值，包括负介电常数和磁导率。进一步的挑战是相对于波长的大尺寸结构和几何形状的复杂性。为了克服这些挑战并实现三维光学复合材料结构的严格和高效的电磁建模，我们开发了一种并行实现的多层快速多极算法（MLFMA）。用所谓的“电、磁电流联合场积分方程”实现了复合结构的精确表述。采用分段线性基函数对曲面积分方程进行精细离散，并采用并行MLFMA迭代求解密集矩阵方程。在分布式内存架构下，采用分层策略实现MLFMA的高效并行化。在本文中，为了证明所提出的电磁求解器的能力，给出了大规模正则和复杂的现实问题的快速准确的解，例如光学超材料，离散与数以千万计的未知数。
Accurate electromagnetic modeling of complicated optical structures poses several challenges. Optical metamaterial and plasmonic structures are composed of multiple coexisting dielectric and/or conducting parts. Such composite structures may possess diverse values of conductivities and dielectric constants, including negative permittivity and permeability. Further challenges are the large sizes of the structures with respect to wavelength and the complexities of the geometries. In order to overcome these challenges and to achieve rigorous and efficient electromagnetic modeling of three-dimensional optical composite structures, we have developed a parallel implementation of the multilevel fast multipole algorithm (MLFMA). Precise formulation of composite structures is achieved with the so-called "electric and magnetic current combined-field integral equation." Surface integral equations are carefully discretized with piecewise linear basis functions, and the ensuing dense matrix equations are solved iteratively with parallel MLFMA. The hierarchical strategy is used for the efficient parallelization of MLFMA on distributed-memory architectures. In this paper, fast and accurate solutions of large-scale canonical and complicated real-life problems, such as optical metamaterials, discretized with tens of millions of unknowns are presented in order to demonstrate the capabilities of the proposed electromagnetic solver.