O ( n ) COMPLEXITY RANDOMIZED 3D DIRECT SOLVER WITH HSS2D STRUCTURE
O ( n ) COMPLEXITY RANDOMIZED 3D DIRECT SOLVER WITH HSS2D STRUCTURE
复制标题
具有 HSS2D 结构的 O ( n ) 复杂度随机 3D 直接求解器
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
J. Xia
中科院分区：
文献类型：
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作者：
J. Xia
.我们提出了二维HSS（HSS2D）结构来处理大型离散偏微分方程的直接解中的稠密Schur补，对于具有低秩性质的椭圆和Helmholtz偏微分方程等问题，该结构产生了具有O（n）复杂度和O（n）存储的完全结构化随机3D直接解.现有的结构矩阵通常使用稠密生成元。在这里，密集生成器的HSS或低秩结构被进一步利用以产生多层结构，因此我们可以显着提高3D问题的效率。HSS2D结构可以方便地处理3D分解中对应于2D界面的稠密Schur补以及2D离散矩阵的逆。多层的随机化被认为是，并显示各种HSS2D算法。
. We propose two dimensional HSS (HSS2D) structures for handling dense Schur complements in the direct solutions of large discretized PDEs, which yields fully structured randomized 3D direct solvers with about O ( n ) complexity and O ( n ) storage for problems such as elliptic and Helmholtz PDEs with the low-rank property. Existing structured matrices usually use dense generators. Here, HSS or low-rank structures of the dense generators are further exploited to yield multi-layer structures, so that we can significantly improve the e � ciency for 3D problems. Dense Schur complements corresponding to 2D interfaces in 3D factorizations as well as inverses of 2D discretized matrices can be handled conveniently with HSS2D structures. Multiple layers of randomization is considered, and various HSS2D algorithms are shown.