Year: 2021
Author: Jiuyang Liang, Zixuan Gao, Zhenli Xu
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 5 : pp. 1126–1141
Abstract
Approximation of interacting kernels by sum of Gaussians (SOG) is frequently required in many applications of scientific and engineering computing in order to construct efficient algorithms for kernel summation or convolution problems. In this paper, we propose a kernel-independent SOG method by introducing the de la Vallée-Poussin sum and Chebyshev polynomials. The SOG works for general interacting kernels and the lower bound of Gaussian bandwidths is tunable and thus the Gaussians can be easily summed by fast Gaussian algorithms. The number of Gaussians can be further reduced via the model reduction based on the balanced truncation based on the square root method. Numerical results on the accuracy and model reduction efficiency show attractive performance of the proposed method.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0254
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 5 : pp. 1126–1141
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Sum-of-Gaussians approximation interaction kernels de la Vallée-Poussin sums model reduction.
Author Details
-
Random Batch Sum-of-Gaussians Method for Molecular Dynamics Simulations of Particle Systems
Liang, Jiuyang | Xu, Zhenli | Zhou, QiSIAM Journal on Scientific Computing, Vol. 45 (2023), Iss. 5 P.B591
https://doi.org/10.1137/22M1497201 [Citations: 2] -
A Kernel-Independent Sum-of-Exponentials Method
Gao, Zixuan | Liang, Jiuyang | Xu, ZhenliJournal of Scientific Computing, Vol. 93 (2022), Iss. 2
https://doi.org/10.1007/s10915-022-01999-1 [Citations: 2]