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首页> 外文期刊>Journal of Computational Physics >An efficient hybrid MLFMA-FFT solver for the volume integral equation in case of sparse 3D inhomogeneous dielectric scatterers
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An efficient hybrid MLFMA-FFT solver for the volume integral equation in case of sparse 3D inhomogeneous dielectric scatterers

机译：稀疏3D非均匀介质散射体的体积积分方程的高效混合MLFMA-FFT求解器

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Electromagnetic scattering problems involving inhomogeneous objects can be numerically solved by applying a Method of Moments discretization to the volume integral equation. For electrically large problems, the iterative solution of the resulting linear system is expensive, both computationally and in memory use. In this paper, a hybrid MLFMA-FFT method is presented, which combines the fast Fourier transform (FFT) method and the High Frequency Multilevel Fast Multipole Algorithm (MLFMA) in order to reduce the cost of the matrix-vector multiplications needed in the iterative solver. The method represents the scatterers within a set of possibly disjoint identical cubic subdomains, which are meshed using a uniform cubic grid. This specific mesh allows for the application of FFTs to calculate the near interactions in the MLFMA and reduces the memory cost considerably, since the aggregation and disaggregation matrices of the MLFMA can be reused. Additional improvements to the general MLFMA framework, such as an extention of the FFT interpolation scheme of Sarvas et al. from the scalar to the vectorial case in combination with a more economical representation of the radiation patterns on the lowest level in vector spherical harmonics, are proposed and the choice of the subdomain size is discussed. The hybrid method performs better in terms of speed and memory use on large sparse configurations than both the FFT method and the HF MLFMA separately and it has lower memory requirements on general large problems. This is illustrated on a number of representative numerical test cases. (C) 2008 Elsevier Inc. All rights reserved.
机译：通过将矩量离散化方法应用于体积积分方程，可以数值解决涉及不均匀物体的电磁散射问题。对于电气大问题，无论是在计算上还是在内存使用上，所得线性系统的迭代解决方案都是昂贵的。本文提出了一种混合的MLFMA-FFT方法，该方法结合了快速傅立叶变换（FFT）方法和高频多级快速多极子算法（MLFMA），以减少迭代中所需的矩阵向量乘法的成本解算器。该方法表示在一组可能不相交的相同立方子域中的散射体，这些子域使用统一的立方网格进行网格划分。这种特定的网格允许FFT的应用来计算MLFMA中的近距离相互作用，并显着降低存储成本，因为可以重复使用MLFMA的聚集和分解矩阵。对通用MLFMA框架的其他改进，例如Sarvas等人的FFT插值方案的扩展。提出了从标量到矢量情况的组合，并结合了更经济的矢量球形谐波最低水平辐射方向图表示，并讨论了子域大小的选择。与单独的FFT方法和HF MLFMA相比，混合方法在大型稀疏配置上的速度和内存使用方面表现更好，并且在一般的大问题上具有较低的内存要求。许多代表性的数字测试案例都对此进行了说明。 （C）2008 Elsevier Inc.保留所有权利。

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