Massively parallel structured multifrontal solver for time-harmonic elastic waves in 3-D anisotropic media
Massively parallel structured multifrontal solver for time-harmonic elastic waves in 3-D anisotropic media
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DOI：
10.1111/j.1365-246x.2012.05634.x
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发表时间：
2012-10
影响因子：
2.8
通讯作者：
Shen Wang;M. V. Hoop;J. Xia;X. Li
中科院分区：
文献类型：
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作者：
Shen Wang;M. V. Hoop;J. Xia;X. Li
我们提出了一个描述三维各向异性介质时谐弹性波方程的大规模并行结构多正面求解器。我们使用了多分量二阶有限差分方法。我们扩展了相应的模板，在不增加阶数的情况下提高了离散化的精度。这种精度与我们求解器底层的层次半可分性（HSS）低秩矩阵压缩所使用的容差级别一致。有限精度离散化和有限精度矩阵求解之间的相互作用产生了关键策略，这导致了我们算法的体系结构。我们分析了相关的矩阵结构，（数值）估计了密集矩阵在HSS压缩前的秩，研究了各向异性的影响，并推导了算法的复杂度和存储要求。
SUMMARY We present a massively parallel structured multifrontal solver for the equations describing time-harmonic elastic waves in 3-D anisotropic media. We use a multicomponent second-order finite-difference method. We extend the corresponding stencil to enhance the accuracy of the discretization without increasing the order. This accuracy is aligned with the tolerance level used for the Hierarchically SemiSeparable (HSS) low rank matrix compression underlying our solver. The interplay between the finite accuracy discretization and the finite accuracy matrix solver yields the key strategy which leads to the architecture of our algorithm. We analyse the relevant matrix structures, (numerically) estimate the rank of the dense matrices prior to the HSS compression and study the effect of anisotropy, and deduce the complexity and storage requirements of our algorithm.