A Fourier-series-based kernel-independent fast multipole method
| Autor: | Nikos P. Pitsianis, Jingfang Huang, Bo Zhang, Xiaobai Sun |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Applied Mathematics Fast multipole method Diagonal MathematicsofComputing_NUMERICALANALYSIS Computer Science::Numerical Analysis Computer Science Applications Translation operator Computational Mathematics symbols.namesake Operator (computer programming) Modeling and Simulation Kernel (statistics) Green's function Computer Science::Mathematical Software Calculus symbols Multipole expansion Algorithm Fourier series Mathematics |
| Zdroj: | Journal of Computational Physics. 230:5807-5821 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2011.03.049 |
| Popis: | We present in this paper a new kernel-independent fast multipole method (FMM), named as FKI-FMM, for pairwise particle interactions with translation-invariant kernel functions. FKI-FMM creates, using numerical techniques, sufficiently accurate and compressive representations of a given kernel function over multi-scale interaction regions in the form of a truncated Fourier series. It provides also economic operators for the multipole-to-multipole, multipole-to-local, and local-to-local translations that are typical and essential in the FMM algorithms. The multipole-to-local translation operator, in particular, is readily diagonal and does not dominate in arithmetic operations. FKI-FMM provides an alternative and competitive option, among other kernel-independent FMM algorithms, for an efficient application of the FMM, especially for applications where the kernel function consists of multi-physics and multi-scale components as those arising in recent studies of biological systems. We present the complexity analysis and demonstrate with experimental results the FKI-FMM performance in accuracy and efficiency. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect