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compactly supported radial basis functions for solving certain high order partial differential equations in 3D

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2015年 55卷 2-9页

作者： Li, Wen Li, Ming Chen, C. S. Liu, Xiaofeng Taiyuan Univ Technol Coll Math Taiyuan 030024 Peoples R China Univ So Mississippi Dept Math Hattiesburg MS 39406 USA

compactly supported radial basis functions have been selected as basis functions for the derivation of closed-form particular solution in the process of solving certain high order partial differential equations in 3D. The method of particular solutions and the method of fundamental solutions are employed to numerically evaluate the particular solution and homogeneous solution of a 3D problem. Two numerical examples are given to demonstrate that the proposed method is applicable for handling large-scale problems. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： compactly supported radial basis functions The method of particular solutions The method of fundamental solutions Particular solution Homogeneous solution Plate vibration equation

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A meshless scaling iterative algorithm based on compactly supported radial basis functions for the numerical solution of Lane-Emden-Fowler equation

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NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 2012年第2期28卷 554-572页

作者： Shen, Quan Peking Univ Sch Math Sci Beijing 100871 Peoples R China

In this article, we combine the compactly supported radial basis function (RBF) collocation method and the scaling iterative algorithm to compute and visualize the multiple solutions of the Lane-Emden-Fowler equation on a bounded domain Omega subset of R-2 with a homogeneous Dirichlet boundary condition. This novel method has the advantage over traditional methods, which approximate the spatial derivatives using either the finite difference method (FDM), the finite element method (FEM), or the boundary element method (BEM), because it does not require a mesh over the domain. As a result, it needs less computational time than the globally supported RBF collocation method. When compared with the reference solutions in (Chen, Zhou, and Ni, Int J Bifurcation Chaos 10 (2000), 565-1612), our numerical results demonstrate the accuracy and ease of implementation of this method. It is therefore much more suitable for dealing with the complex domains than the FEM, the FDM, and the BEM. (c) 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 554-572, 2012

关键词： compactly supported radial basis functions meshless collocation method scaling iterative algorithm

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Multistep scattered data interpolation using compactly supported radial basis functions

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 1996年第1-2期73卷 65-78页

作者： Floater, MS Iske, A SINTEF N-0314 OSLO NORWAY

A hierarchical scheme is presented for smoothly interpolating scattered data with radial basis functions of compact support. A nested sequence of subsets of the data is computed efficiently using successive Delaunay triangulations. The scale of the basis function at each level is determined from the current density of the points using information from the triangulation. The method is rotationally invariant and has good reproduction properties. Moreover the solution can be calculated and evaluated in acceptable computing time.

关键词： hierarchical interpolation scattered data compactly supported radial basis functions

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Evaluation of Geometric Complementarity between Molecular Surfaces Using compactly supported radial basis functions

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2009年第4期6卷 689-694页

作者： Diago, Luis A. Moreno, Ernesto Tokyo Inst Technol Dept Mech Sci & Engn Meguro Ku Tokyo Japan Ctr Mol Immunol Havana 11600 Cuba

One of the challenges faced by all molecular docking algorithms is that of being able to discriminate between correct results and false positives obtained in the simulations. The scoring or energetic function is the one that must fulfill this task. Several scoring functions have been developed and new methodologies are still under development. In this paper, we have employed the compactly supported radial basis functions (CSRBF) to create analytical representations of molecular surfaces, which are then included as key components of a new scoring function for molecular docking. The method proposed here achieves a better ranking of the solutions produced by the program DOCK, as compared with the ranking done by its native contact scoring function. Our new analytical scoring function based on CSRBF can be easily included in different available docking programs as a reliable and quick filter in large-scale docking simulations.

关键词： Molecular docking compactly supported radial basis functions

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A well-conditioned and efficient Levin method for highly oscillatory integrals with compactly supported radial basis functions

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2021年 131卷 51-63页

作者： Khan, Suliman Zaman, Sakhi Arshad, Muhammad Kang, Hongchao Shah, Hasrat Hussain Issakhov, Alibek Cent South Univ Sch Math & Stat Changsha 410083 Hunan Peoples R China Univ Engn & Technol Fac Architecture Allied Sci & Humanities Peshawar Pakistan Abbottabad Univ Sci & Technol Dept Math Abbottabad Pakistan Hangzhou Dianzi Univ Sch Sci Dept Math Hangzhou 310018 Zhejiang Peoples R China Balochistan Univ Informat Technol Engn & Manageme Dept Math Sci Quetta Pakistan Al Farabi Kazakh Natl Univ Dept Math & Comp Modelling Alma Ata 050040 Kazakhstan Kazakh British Tech Univ Dept Math & Cybernet Alma Ata 050000 Kazakhstan

Highly oscillatory integrals are frequently involved in applied problems, particularly for large-scale data and high frequencies. Levin method with global radial basis functions was implemented for numerical evaluation of these integrals in the literature. However, when the frequency is large or nodal points are increased, the Levin method with global radial basis functions faces several issues such as large condition number of the interpolation matrix and computationally inefficiency of the method, etc. In this paper, the Levin method with compactly supported radial basis functions is proposed to handle deficiencies of the method. In addition, theoretical error bounds and stability analysis of the proposed methods are performed. Several numerical examples are included to verify the accuracy, efficiency, and well-conditioned behavior of the proposed methods.

关键词： Highly oscillatory integrals compactly supported radial basis functions Stable algorithms Levin method Hybrid functions

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Method of fundamental solutions for 3D elasticity with body forces by coupling compactly supported radial basis functions

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2015年 60卷 123-136页

作者： Lee, Cheuk-Yu Wang, Hui Qin, Qing-Hua Australian Natl Univ Res Sch Engn Acton ACT 2601 Australia Henan Univ Technol Dept Engn Mech Zhengzhou 450001 Peoples R China

In this paper, a meshless computational model by integrating the method of fundamental solutions (MFS) and the method of particular solutions fulfilled with compactly supported radial basis functions (CSRBF) is developed for three-dimensional (3D) linear elasticity with the presence of body forces. The corresponding displacement and stress particular solution kernels across the support radius are firstly derived using Galerkin vectors and then are used to modify the boundary conditions. Subsequently, the classical meshless MFS, in which the homogeneous part of the full solutions are approximated using the linear combination of displacement and stress fundamental solutions in 3D linear elasticity, is formulated for solving the homogeneous 3D linear elastic system. Finally, several examples are presented to demonstrate the accuracy and efficiency of the present meshless method and also the effect of sparseness of interpolation matrix in CSRBF interpolation is discussed. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Three-dimensional linear elasticity Method of fundamental solutions Particular solutions compactly supported radial basis functions

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Approximate implicitization of parametric surfaces by using compactly supported radial basis functions

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2008年第12期56卷 3064-3069页

作者： Wu, Jinming Wang, Renhong Zhejiang Gongshang Univ Coll Stat & Math Hangzhou 310018 Peoples R China Dalian Univ Technol Inst Math Sci Dalian 116024 Peoples R China

In this paper, a new approach is proposed to solve the approximate implicitization of parametric surfaces. it is primarily based on multivariate interpolation of scattered data by using compactly supported radial basis functions. Experimental results are provided to illustrate the proposed method is flexible and effective. Crown Copyright (c) 2008 Published by Elsevier Ltd. All rights reserved.

关键词： Approximate implicitization Parametric surfaces compactly supported radial basis functions Boundary constraint points Normal constraint points

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Dual reciprocity boundary element method using compactly supported radial basis functions for 3D linear elasticity with body forces

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INTERNATIONAL JOURNAL OF MECHANICS AND MATERIALS IN DESIGN 2016年第4期12卷 463-476页

作者： Lee, Cheuk-Yu Wang, Hui Qin, Qing-Hua Australian Natl Univ Res Sch Engn Acton ACT 2601 Australia Henan Univ Technol Dept Engn Mech Zhengzhou 450001 Peoples R China

A new computational model by integrating the boundary element method and the compactly supported radial basis functions (CSRBF) is developed for three-dimensional (3D) linear elasticity with the presence of body forces. The corresponding displacement and stress particular solution kernels across the supported radius in the CSRBF are obtained for inhomogeneous term interpolation. Subsequently, the classical dual reciprocity boundary element method, in which the domain integrals due to the presence of body forces are transferred into equivalent boundary integrals, is formulated by introducing locally supported displacement and stress particular solution kernels for solving the inhomogeneous 3D linear elastic system. Finally, several examples are presented to demonstrate the accuracy and efficiency of the present method.

关键词： Three-dimensional linear elasticity Dual reciprocity method Boundary element method compactly supported radial basis functions

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Closed form representations for a class of compactly supported radial basis functions

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ADVANCES IN COMPUTATIONAL MATHEMATICS 2012年第1期36卷 115-136页

作者： Hubbert, Simon Birkbeck Coll Sch Econ Math & Stat London WC1E 7HX England

In this paper we re-examine Wendland's strategy for the construction of compactly supported positive definite radial basis functions. We acknowledge that this strategy can be modified to capture a much larger range of functions, including the so-called missing Wendland functions which have been the subject of a recent paper by Schaback (Adv Comput Math 34:67-81, 2011). Our approach is to focus on a general integral representation of such functions and we will show how a careful evaluation of this integral leads to new closed form expressions for both Wendland's original functions and the missing ones. The resulting expressions are easy to code and so provide the potential user with a quick way of accessing a desired example for a given application.

关键词： Positive definite functions compactly supported radial basis functions Hypergeometric functions Associated Legendre functions

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Two new classes of compactly supported radial basis functions for approximation of discrete and continuous data

ENGINEERING REPORTS

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ENGINEERING REPORTS 2019年第1期1卷

作者： Meira Menandro, Fernando Cesar Univ Fed Espirito Santo Mech Engn Dept Vitoria ES Brazil Av Fernando Ferrari 514 BR-29075910 Vitoria ES Brazil

radial basis functions (RBFs), first proposed for interpolation of scattered data, have gotten the scientific community interest in the past two decades, with applications ranging from interpolation with the dual reciprocity approach of the boundary element method to mesh-free finite element applications. The use of compactly supported RBFs (CSRBFs) has spread due to their localization properties. However, the mathematical derivation of continuous polynomial functions for different continuity requirements can be quite cumbersome, and although a few classes of functions have already been proposed, there is still room for nonpolynomial trial functions. In this paper, two new classes of CSRBFs are presented for which the continuity requirements are guaranteed. To justify the novelty claim, a view of RBF literature is conducted. The first function class proposed consists of a combination of different inverse polynomial functions, similar to inverse quadric functions, and is thus called inverse class. The second class is called the rational class, in which the functions are obtained as a ratio of two polynomial functions. The proposed functions are used on an approximation software, which takes advantage of their simplicity. The results demonstrate the accuracy and convergence of the proposed functions when compared to some referenced CSRBFs.

关键词： approximation compactly supported radial basis functions least squares methods nonpolynomial radial basis functions

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