多层快速多极子方法的快速插值
FAST INTERPOLATION FOR MULTILEVEL FAST MULTIPOLE METHOD
查看参考文献12篇
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文摘
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多层快速多极子方法(MLFMM)可用来加速迭代求解由Maxwell方程组或Helmholtz方程导出的积分方程, 其复杂度理论上是O(NlogN), N为未知量个数.MLFMM依赖于快速计算每层的转移项, 以及上聚和下推过程中的层间插值.本文引入计算类似Ⅳ体问题的一维快速多极子方法(FMMlD).基于FMMlD的快速Lagrange插值算法可将转移项的计算复杂度由 O(N~(1.5))降低到O(N).运用FMMlD与FFT混合的快速谱插值算法可将层间插值的计算复杂度由O(K~2)降低到O(KlogK), K为插值取样点数.数值结果显示了基于这两种快速插值的 MLFMM具有近似线性的时间复杂度 |
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其他语种文摘
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Multilevel fast multipole method (MLFMM) can be used to accelerate the iterative solution of integral equation deduced from Maxwell equations or Helmholtz-type equation, with a theoretical complexity of 0(N log N), where N is the number of unknowns. MLFMM depends on fast calculating the translation term at each level, and interpolations between levels during upward and downward pass phases. The one-dimentional fast multipole method (FMM1D) similar to which used in N-body problem is introduced in this paper. Fast Lagrange interpolation algorithm based on FMM1D can reduce the computing time of translation operator from O(N1.5) to O(N). Fast spectrum interpolation with a hybrid FFT-FMM1D method can also reduce the computing complexity of interpolations between levels from O(K2) to O(KlogK), where K is the number of sample points. The numerical results of MLFMM based on these two fast inperpolation methods have near linear time performances and accurate solutions |
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来源
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计算数学
,2011,33(2):145-156 【核心库】
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关键词
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积分方程
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多层快速多极子方法
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转移项
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快速Lagrange插值
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快速谱插值
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地址
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中国科学院计算机网络信息中心超级计算中心, 北京, 100190
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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0254-7791 |
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学科
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数学 |
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基金
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国家自然科学基金
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国家高技术研究发展计划
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国家973计划
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文献收藏号
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CSCD:4181593
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