A SVD Accelerated Kernel-independent Fast
Multipole Method And Its Application To BEM
Author(s)
Yanchuang Cao, Lihua Wen & Junjie Rong
Abstract
The kernel-independent fast multipole method (KIFMM) proposed by L. Ying
et al. is of almost linear complexity. In the original KIFMM the time-consuming
M2L translations are accelerated by FFT. However, when more equivalent points
are used to achieve higher accuracy, the efficiency of the FFT approach tends to
be lower because more auxiliary volume grid points have to be added. In this
paper, all the translations of the KIFMMare accelerated by using the singular value
decomposition (SVD) based on the low-rank property of the translating matrices.
The acceleration of M2L is realized by first transforming the associated translating
matrices into more compact form, and then using low-rank approximations. By
using the transform matrices for M2L, the orders of the translating matrices in
upward and downward passes are also reduced. The improved KIFMM is then
applied to accelerate BEM. Numerical results show that, compared with the
original KIFMM, the present method can reduce about 40% of the iterating time
and 25% of the memory requirement.
Keywords: boundary element method, kernel-independent fast multipole method,
singular value decomposition, matrix compression.
Keywords
boundary element method, kernel-independent fast multipole method,
singular value decomposition, matrix compression
Related Book
Other papers in this volume
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