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首页> 外文期刊>Antennas and Propagation, IEEE Transactions on >Layered ${cal H}$-Matrix Based Inverse and LU Algorithms for Fast Direct Finite-Element-Based Computation of Electromagnetic Problems
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Layered ${cal H}$-Matrix Based Inverse and LU Algorithms for Fast Direct Finite-Element-Based Computation of Electromagnetic Problems

机译：基于分层 $ {cal H} $ -矩阵的逆和LU算法，用于基于电磁场的快速直接有限元计算

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摘要

A layered ${cal H}$ -matrix based inverse algorithm and a layered ${cal H}$-matrix based LU factorization and solution algorithm are developed to accelerate the direct solution of the finite element matrix resulting from electromagnetics-based analysis of general 3-D problems. In these algorithms, the direct solution of the original 3-D system matrix is transformed to the direct solution of multiple 2-D problems. The size of the matrix to be computed is thus reduced from a 3-D size to a 2-D size. Moreover, the growth rate of the rank of the inverse finite element matrix with electric size is reduced from a 3-D based growth rate to a 2-D based growth rate. Numerical experiments have demonstrated the clear advantages of the proposed direct solvers over a state-of-the-art multifrontal based direct sparse solver as well as existing fast ${cal H}$-matrix based direct solvers, in both CPU time and memory consumption, for finite-element analysis of general 3-D electromagnetic problems.
机译：分层的 $ {cal H} $ -基于矩阵的逆算法和分层的 $ {cal H} $ -矩阵的LU分解和求解算法，以加速基于电磁的一般3的分析产生的有限元矩阵的直接求解。 D问题。在这些算法中，将原始3-D系统矩阵的直接解转换为多个2-D问题的直接解。因此，要计算的矩阵的大小从3D大小减小为2D大小。而且，具有电尺寸的逆有限元矩阵的秩的增长率从基于3D的增长率降低到基于二维的增长率。数值实验证明了所提出的直接求解器相对于基于最新技术的基于多前沿的直接稀疏求解器以及现有的快速 $ {cal基于H} $ -矩阵的直接求解器，在CPU时间和内存消耗方面，都可以用于一般3-D电磁问题的有限元分析。

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