The black-box fast multipole method
The black-box fast multipole method
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DOI：
10.1016/j.jcp.2009.08.031
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发表时间：
2009-12-10
影响因子：
4.1
通讯作者：
Darve, Eric
中科院分区：
文献类型：
--
作者：
Fong, William;Darve, Eric
提出了一种新的O（N）快速多极子公式的非振荡核。该算法适用于仅在数值上已知的核K（x，y），即对于任何（x，y）都可以获得它们的数值。这与许多快速多极方法完全不同，这些方法依赖于K的远场行为的解析展开，对于垂直杆x-y垂直杆大。其他的“黑箱”或“核独立”快速多极子方法已经被设计出来。我们的方法的优点是，即使对于非常大的系统，也需要很小的预计算时间，并且对于给定的L-2近似公差误差，使用最少数量的系数来表示远场。这种技术可以是非常有用的问题的核心是已知的分析，但相当复杂，或为内核的定义是纯粹的数字。(C)2009 Elsevier Inc. All rights reserved.
A new O(N) fast multipole formulation is proposed for non-oscillatory kernels. This algorithm is applicable to kernels K(x,y) which are only known numerically, that is their numerical value can be obtained for any (x,y). This is quite different from many fast multipole methods which depend on analytical expansions of the far-field behavior of K, for vertical bar x - y vertical bar large. Other "black-box" or "kernel-independent" fast multipole methods have been devised. Our approach has the advantage of requiring a small pre-computation time even for very large systems, and uses the minimal number of coefficients to represent the far-field, for a given L-2 tolerance error in the approximation. This technique can be very useful for problems where the kernel is known analytically but is quite complicated, or for kernels which are defined purely numerically. (C) 2009 Elsevier Inc. All rights reserved.