Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid Integral equations in electromagnetics
Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid Integral equations in electromagnetics
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DOI：
10.1109/tap.2004.834084
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发表时间：
2004-09
影响因子：
5.7
通讯作者：
Jeonghwa Lee;Jun Zhang;Caicheng Lu
中科院分区：
文献类型：
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作者：
Jeonghwa Lee;Jun Zhang;Caicheng Lu
在计算电磁学中，多层快速多极子算法（MLFMA）被用来降低矩阵向量积运算的计算复杂度。在迭代求解离散混合积分方程组的稠密线性方程组时，采用稀疏近似逆（SAI）预处理技术来加快Krylov迭代的收敛速度.我们表明，一个良好的质量SAI预处理器可以通过使用数值生成的MLFMA的近部矩阵。本研究的主要目的是表明此类SAI预处理器对于MLFMA是有效的，并且可以大幅减少Krylov迭代的次数。实验结果表明，SAI预处理的MLFMA保持了MLFMA的计算复杂度，但收敛速度快得多，从而有效地减少了整体仿真时间。
In computational electromagnetics, the multilevel fast multipole algorithm (MLFMA) is used to reduce the computational complexity of the matrix vector product operations. In iteratively solving the dense linear systems arising from discretized hybrid integral equations, the sparse approximate inverse (SAI) preconditioning technique is employed to accelerate the convergence rate of the Krylov iterations. We show that a good quality SAI preconditioner can be constructed by using the near part matrix numerically generated in the MLFMA. The main purpose of this study is to show that this class of the SAI preconditioners are effective with the MLFMA and can reduce the number of Krylov iterations substantially. Our experimental results indicate that the SAI preconditioned MLFMA maintains the computational complexity of the MLFMA, but converges a lot faster, thus effectively reduces the overall simulation time.