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Research Advances on the Collocation Methods Based on the PhysicalInformed Kernel Functions
Zhuojia Fu1,*, Qiang Xi2, Wenzhi Xu1
1 College of Mechanics and Materials, Hohai University, Nanjing, 211100, China
2 College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing, 210098, China
* Corresponding Author: Zhuojia Fu. Email:
The International Conference on Computational & Experimental Engineering and Sciences 2023, 27(1), 1-1. https://doi.org/10.32604/icces.2023.09393
Abstract
In the past few decades, although traditional computational methods such as finite element have been
successfully used in many scientific and engineering fields, they still face several challenging problems such
as expensive computational cost, low computational efficiency, and difficulty in mesh generation in the
numerical simulation of wave propagation under infinite domain, large-scale-ratio structures, engineering
inverse problems and moving boundary problems. This paper introduces a class of collocation discretization
techniques based on physical-informed kernel function (PIKF) to efficiently solve the above-mentioned
problems. The key issue in the physical-informed kernel function collocation methods (PIKFCMs) is to
construct the related basis functions, which includes the physical information of the considered differential
governing equation. Based on these physical-informed kernel functions (PIKFs), these methods do not
need/only need a few collocation nodes to discretize the considered differential governing equations, which
may effectively improve the computational efficiency. In this paper, several typical physical-informed kernel
functions (PIKFs) that satisfy common-used homogeneous differential equations, such as the fundamental
solutions, the harmonic functions, the radial Trefftz functions and the T-complete functions and so on, are
firstly introduced. After that, the ways to construct the physical-informed kernel functions (PIKFs) for
nonhomogeneous differential equations, inhomogeneous differential equations, unsteady-state differential
equations and implicit differential equations are introduced in turn. Then according to the characteristics of
the considered problems, the global collocation scheme or the localized collocation scheme is selected to
establish the corresponding physical-informed kernel function collocation method (PIKFCM). Finally, four
typical examples are given to verify the effectiveness of the physical-informed kernel function collocation
methods (PIKFCMs) proposed in this paper.
Keywords
Cite This Article
APA Style
Fu, Z., Xi, Q., Xu, W. (2023). Research advances on the collocation methods based on the physicalinformed kernel functions. The International Conference on Computational & Experimental Engineering and Sciences, 27(1), 1-1. https://doi.org/10.32604/icces.2023.09393
Vancouver Style
Fu Z, Xi Q, Xu W. Research advances on the collocation methods based on the physicalinformed kernel functions. Int Conf Comput Exp Eng Sciences . 2023;27(1):1-1 https://doi.org/10.32604/icces.2023.09393
IEEE Style
Z. Fu, Q. Xi, and W. Xu "Research Advances on the Collocation Methods Based on the PhysicalInformed Kernel Functions," Int. Conf. Comput. Exp. Eng. Sciences , vol. 27, no. 1, pp. 1-1. 2023. https://doi.org/10.32604/icces.2023.09393