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Numerical Simulation of Dam-Break Flows Using Radial Basis Functions: Application to Urban Flood Inundation
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作者 Abdoulhafar Halassi Bacar Said Charriffaini Rawhoudine 《American Journal of Computational Mathematics》 2024年第3期318-332,共15页
Dam-break flows pose significant threats to urban areas due to their potential for causing rapid and extensive flooding. Traditional numerical methods for simulating these events struggle with complex urban landscapes... Dam-break flows pose significant threats to urban areas due to their potential for causing rapid and extensive flooding. Traditional numerical methods for simulating these events struggle with complex urban landscapes. This paper presents an alternative approach using Radial Basis Functions to simulate dam-break flows and their impact on urban flood inundation. The proposed method adapts a new strategy based on Particle Swarm Optimization for variable shape parameter selection on meshfree formulation to enhance the numerical stability and convergence of the simulation. The method’s accuracy and efficiency are demonstrated through numerical experiments, including well-known partial and circular dam-break problems and an idealized city with a single building, highlighting its potential as a valuable tool for urban flood risk management. 展开更多
关键词 Dam-Break Flows Numerical Simulation Shallow Water Equations radial basis functions Urban Flood Inundation
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A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems
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作者 Scott A. Sarra Derek Musgrave +1 位作者 Marcus Stone Joseph I. Powell 《Journal of Applied Mathematics and Physics》 2024年第7期2559-2573,共15页
Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with... Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used. 展开更多
关键词 Numerical Partial Differential Equations Boundary Value Problems radial basis function Methods Ghost Points Variable Shape Parameter Least Squares
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A Numerical Method for Solving Ill-Conditioned Equation Systems Arising from Radial Basis Functions
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作者 Edward J. Kansa 《American Journal of Computational Mathematics》 2023年第2期356-370,共15页
Continuously differentiable radial basis functions (C<sup>∞</sup>-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices are ... Continuously differentiable radial basis functions (C<sup>∞</sup>-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices are full and can become very ill- conditioned. Similarly, the Hilbert and Vandermonde have full matrices and become ill-conditioned. The difference between a coefficient matrix generated by C<sup>∞</sup>-RBFs for partial differential or integral equations and Hilbert and Vandermonde systems is that C<sup>∞</sup>-RBFs are very sensitive to small changes in the adjustable parameters. These parameters affect the condition number and solution accuracy. The error terrain has many local and global maxima and minima. To find stable and accurate numerical solutions for full linear equation systems, this study proposes a hybrid combination of block Gaussian elimination (BGE) combined with arbitrary precision arithmetic (APA) to minimize the accumulation of rounding errors. In the future, this algorithm can execute faster using preconditioners and implemented on massively parallel computers. 展开更多
关键词 Continuously Differentiable radial basis functions Global Maxima and Minima Solutions of Ill-Conditioned Linear Equations Block Gaussian Elimination Arbitrary Precision Arithmetic
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Crack Fault Diagnosis and Location Method for a Dual-Disk Hollow Shaft Rotor System Based on the Radial Basis Function Network and Pattern Recognition Neural Network 被引量:2
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作者 Yuhong Jin Lei Hou +1 位作者 Zhenyong Lu Yushu Chen 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2023年第2期180-197,共18页
The crack fault is one of the most common faults in the rotor system,and researchers have paid close attention to its fault diagnosis.However,most studies focus on discussing the dynamic response characteristics cause... The crack fault is one of the most common faults in the rotor system,and researchers have paid close attention to its fault diagnosis.However,most studies focus on discussing the dynamic response characteristics caused by the crack rather than estimating the crack depth and position based on the obtained vibration signals.In this paper,a novel crack fault diagnosis and location method for a dual-disk hollow shaft rotor system based on the Radial basis function(RBF)network and Pattern recognition neural network(PRNN)is presented.Firstly,a rotor system model with a breathing crack suitable for a short-thick hollow shaft rotor is established based on the finite element method,where the crack's periodic opening and closing pattern and different degrees of crack depth are considered.Then,the dynamic response is obtained by the harmonic balance method.By adjusting the crack parameters,the dynamic characteristics related to the crack depth and position are analyzed through the amplitude-frequency responses and waterfall plots.The analysis results show that the first critical speed,first subcritical speed,first critical speed amplitude,and super-harmonic resonance peak at the first subcritical speed can be utilized for the crack fault diagnosis.Based on this,the RBF network and PRNN are adopted to determine the depth and approximate location of the crack respectively by taking the above dynamic characteristics as input.Test results show that the proposed method has high fault diagnosis accuracy.This research proposes a crack detection method adequate for the hollow shaft rotor system,where the crack depth and position are both unknown. 展开更多
关键词 Hollow shaft rotor Breathing crack radial basis function network Pattern recognition neural network Machine learning
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A Novel Radial Basis Function Neural Network Approach for ECG Signal Classification
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作者 S.Sathishkumar R.Devi Priya 《Intelligent Automation & Soft Computing》 SCIE 2023年第1期129-148,共20页
ions in the ECG signal.The cardiologist and medical specialistfind numerous difficulties in the process of traditional approaches.The specified restrictions are eliminated in the proposed classifier.The fundamental ai... ions in the ECG signal.The cardiologist and medical specialistfind numerous difficulties in the process of traditional approaches.The specified restrictions are eliminated in the proposed classifier.The fundamental aim of this work is tofind the R-R interval.To analyze the blockage,different approaches are implemented,which make the computation as facile with high accuracy.The information are recovered from the MIT-BIH dataset.The retrieved data contain normal and pathological ECG signals.To obtain a noiseless signal,Gaborfilter is employed and to compute the amplitude of the signal,DCT-DOST(Discrete cosine based Discrete orthogonal stock well transform)is implemented.The amplitude is computed to detect the cardiac abnormality.The R peak of the underlying ECG signal is noted and the segment length of the ECG cycle is identified.The Genetic algorithm(GA)retrieves the primary highlights and the classifier integrates the data with the chosen attributes to optimize the identification.In addition,the GA helps in performing hereditary calculations to reduce the problem of multi-target enhancement.Finally,the RBFNN(Radial basis function neural network)is applied,which diminishes the local minima present in the signal.It shows enhancement in characterizing the ordinary and anomalous ECG signals. 展开更多
关键词 Electrocardiogram signal gaborfilter discrete cosine based discrete orthogonal stock well transform genetic algorithm radial basis function neural network
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Evolution Performance of Symbolic Radial Basis Function Neural Network by Using Evolutionary Algorithms
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作者 Shehab Abdulhabib Alzaeemi Kim Gaik Tay +2 位作者 Audrey Huong Saratha Sathasivam Majid Khan bin Majahar Ali 《Computer Systems Science & Engineering》 SCIE EI 2023年第10期1163-1184,共22页
Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algor... Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algorithms for training the Symbolic Radial Basis Function Neural Network(SRBFNN)through the behavior’s integration of satisfiability programming.Inspired by evolutionary algorithms,which can iteratively find the nearoptimal solution,different Evolutionary Algorithms(EAs)were designed to optimize the producer output weight of the SRBFNN that corresponds to the embedded logic programming 2Satisfiability representation(SRBFNN-2SAT).The SRBFNN’s objective function that corresponds to Satisfiability logic programming can be minimized by different algorithms,including Genetic Algorithm(GA),Evolution Strategy Algorithm(ES),Differential Evolution Algorithm(DE),and Evolutionary Programming Algorithm(EP).Each of these methods is presented in the steps in the flowchart form which can be used for its straightforward implementation in any programming language.With the use of SRBFNN-2SAT,a training method based on these algorithms has been presented,then training has been compared among algorithms,which were applied in Microsoft Visual C++software using multiple metrics of performance,including Mean Absolute Relative Error(MARE),Root Mean Square Error(RMSE),Mean Absolute Percentage Error(MAPE),Mean Bias Error(MBE),Systematic Error(SD),Schwarz Bayesian Criterion(SBC),and Central Process Unit time(CPU time).Based on the results,the EP algorithm achieved a higher training rate and simple structure compared with the rest of the algorithms.It has been confirmed that the EP algorithm is quite effective in training and obtaining the best output weight,accompanied by the slightest iteration error,which minimizes the objective function of SRBFNN-2SAT. 展开更多
关键词 Satisfiability logic programming symbolic radial basis function neural network evolutionary programming algorithm genetic algorithm evolution strategy algorithm differential evolution algorithm
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Local Radial Basis Function Methods: Comparison, Improvements, and Implementation
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作者 Scott A. Sarra 《Journal of Applied Mathematics and Physics》 2023年第12期3867-3886,共20页
Radial Basis Function methods for scattered data interpolation and for the numerical solution of PDEs were originally implemented in a global manner. Subsequently, it was realized that the methods could be implemented... Radial Basis Function methods for scattered data interpolation and for the numerical solution of PDEs were originally implemented in a global manner. Subsequently, it was realized that the methods could be implemented more efficiently in a local manner and that the local approaches could match or even surpass the accuracy of the global implementations. In this work, three localization approaches are compared: a local RBF method, a partition of unity method, and a recently introduced modified partition of unity method. A simple shape parameter selection method is introduced and the application of artificial viscosity to stabilize each of the local methods when approximating time-dependent PDEs is reviewed. Additionally, a new type of quasi-random center is introduced which may be better choices than other quasi-random points that are commonly used with RBF methods. All the results within the manuscript are reproducible as they are included as examples in the freely available Python Radial Basis Function Toolbox. 展开更多
关键词 radial basis functions Shape Parameter Selection Quasi-Random Centers Numerical PDEs Scientific Computing Open Source Software Python Programming Language Reproducible Research
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SOME PROBLEMS WITH THE METHOD OF FUNDAMENTAL SOLUTION USING RADIAL BASIS FUNCTIONS 被引量:9
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作者 Wang Hui Qin Qinghua 《Acta Mechanica Solida Sinica》 SCIE EI 2007年第1期21-29,共9页
The present work describes the application of the method of fundamental solutions (MFS) along with the analog equation method (AEM) and radial basis function (RBF) approximation for solving the 2D isotropic and ... The present work describes the application of the method of fundamental solutions (MFS) along with the analog equation method (AEM) and radial basis function (RBF) approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson's equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition (SVD) technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric (MQ) are fully analyzed to provide useful reference. 展开更多
关键词 meshless method analog equation method method of fundamental solution radial basis function singular value decomposition Helmholtz equation
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MESHLESS METHOD BASED ON COLLOCATION WITH CONSISTENT COMPACTLY SUPPORTED RADIAL BASIS FUNCTIONS 被引量:3
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作者 宋康祖 张雄 陆明万 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2004年第5期551-557,共7页
Based on our previous study,the accuracy of derivatives of interpolating functions are usually very poor near the boundary of domain when Compactly Supported Radial Basis Functions (CSRBFs)are used,so that it could re... Based on our previous study,the accuracy of derivatives of interpolating functions are usually very poor near the boundary of domain when Compactly Supported Radial Basis Functions (CSRBFs)are used,so that it could result in significant error in solving partial differential equations with Neumann boundary conditions.To overcome this drawback,the Consistent Compactly Supported Radial Basis Functions(CCSRBFs)are developed,which satisfy the predetermined consistency con- ditions.Meshless method based on point collocation with CCSRBFs is developed for solving partial differential equations.Numerical studies show that the proposed method improves the accuracy of approximation significantly. 展开更多
关键词 radial basis function COLLOCATION MESHLESS
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Synchronization of chaos using radial basis functions neural networks 被引量:2
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作者 Ren Haipeng Liu Ding 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2007年第1期83-88,100,共7页
The Radial Basis Functions Neural Network (RBFNN) is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response syst... The Radial Basis Functions Neural Network (RBFNN) is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method. 展开更多
关键词 Chaos synchronization radial basis function neural networks Model error Parameter perturbation Measurement noise.
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HERMITE—BIRKHOFF INTERPOLATION OF SCATTERED DATA BY RADIAL BASIS FUNCTIONS 被引量:6
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作者 吴宗敏 《Analysis in Theory and Applications》 1992年第2期1-10,共10页
For Hermite-Birkhoff interpolation of scattered multidumensional data by radial basis function (?),existence and characterization theorems and a variational principle are proved. Examples include (?)(r)=r^b,Duchon'... For Hermite-Birkhoff interpolation of scattered multidumensional data by radial basis function (?),existence and characterization theorems and a variational principle are proved. Examples include (?)(r)=r^b,Duchon's thin-plate splines,Hardy's multiquadrics,and inverse multiquadrics. 展开更多
关键词 HERMITE BIRKHOFF INTERPOLATION OF SCATTERED DATA BY radial basis functions
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Application of radial basis functions to evolution equations arising in image segmentation 被引量:1
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作者 李淑玲 李小林 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第2期583-588,共6页
In this paper, radial basis functions are used to obtain the solution of evolution equations which appear in variational level set method based image segmentation. In this method, radial basis functions are used to in... In this paper, radial basis functions are used to obtain the solution of evolution equations which appear in variational level set method based image segmentation. In this method, radial basis functions are used to interpolate the implicit level set function of the evolution equation with a high level of accuracy and smoothness. Then, the original initial value problem is discretized into an interpolation problem. Accordingly, the evolution equation is converted into a set of coupled ordinary differential equations, and a smooth evolution can be retained. Compared with finite difference scheme based level set approaches, the complex and costly re-initialization procedure is unnecessary. Numerical examples are also given to show the efficiency of the method. 展开更多
关键词 radial basis functions evolution equations image segmentation RE-INITIALIZATION
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A numerical method based on boundary integral equations and radial basis functions for plane anisotropic thermoelastostatic equations with general variable coefficients 被引量:2
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作者 W.T.ANG X.WANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2020年第4期551-566,共16页
A boundary integral method with radial basis function approximation is proposed for numerically solving an important class of boundary value problems governed by a system of thermoelastostatic equations with variable ... A boundary integral method with radial basis function approximation is proposed for numerically solving an important class of boundary value problems governed by a system of thermoelastostatic equations with variable coe?cients. The equations describe the thermoelastic behaviors of nonhomogeneous anisotropic materials with properties that vary smoothly from point to point in space. No restriction is imposed on the spatial variations of the thermoelastic coe?cients as long as all the requirements of the laws of physics are satis?ed. To check the validity and accuracy of the proposed numerical method, some speci?c test problems with known solutions are solved. 展开更多
关键词 elliptic partial differential equation variable coefficient boundary element method radial basis function anisotropic thermoelastostatics
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Surface Reconstruction of 3D Scattered Data with Radial Basis Functions 被引量:1
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作者 Du XIN-WEI YANG XIAO-YING LIANG XUE-ZHANG 《Communications in Mathematical Research》 CSCD 2010年第2期183-192,共10页
We use Radial Basis Functions (RBFs) to reconstruct smooth surfaces from 3D scattered data. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improveme... We use Radial Basis Functions (RBFs) to reconstruct smooth surfaces from 3D scattered data. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improvements on the methods of surface reconstruction with radial basis functions. A sparse approximation set of scattered data is constructed by reducing the number of interpolating points on the surface. We present an adaptive method for finding the off-surface normal points. The order of the equation decreases greatly as the number of the off-surface constraints reduces gradually. Experimental results are provided to illustrate that the proposed method is robust and may draw beautiful graphics. 展开更多
关键词 radial basis function scattered data implicit surface surface reconstruction
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The Partition of Unity Method for High-Order Finite Volume Schemes Using Radial Basis Functions Reconstruction 被引量:1
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作者 Serena Morigi Fiorella Sgallari 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2009年第2期153-179,共27页
This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equat... This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equations.The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions.The methodology proposed is applied to the noise removal problem in functional surfaces and images.Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence. 展开更多
关键词 Finite volume discretization radial basis functions optimal recovery REGULARIZATION image and surface denoising.
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A Quasi-Interpolation Satisfying Quadratic Polynomial Reproduction with Radial Basis Functions 被引量:1
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作者 Li Zha Renzhong Feng 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2007年第4期348-357,共10页
In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by ... In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by making convolution integral with a constructed spline and a given radial basis function.In particular,for twicely differ- entiable function the proposed method provides better approximation and also takes care of derivatives approximation. 展开更多
关键词 二次方程 多项式 等距处理 数据处理
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Large Scattered Data Fitting Based on Radial Basis Functions 被引量:2
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作者 FENG Ren-zhong XU Liang 《Computer Aided Drafting,Design and Manufacturing》 2007年第1期66-72,共7页
Solving large radial basis function (RBF) interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficult... Solving large radial basis function (RBF) interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficulties, we present a fitting based on radial basis functions satisfying side conditions by least squares, although compared with interpolation the method loses some accuracy, it reduces the computational cost largely. Since the fitting accuracy and the non-singularity of coefficient matrix in normal equation are relevant to the uniformity of chosen centers of the fitted RBE we present a choice method of uniform centers. Numerical results confirm the fitting efficiency. 展开更多
关键词 scattered data radial basis functions interpolation least squares fitting uniform centers
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Analysis of radial basis function interpolation approach 被引量:4
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作者 邹友龙 胡法龙 +3 位作者 周灿灿 李潮流 李长喜 Keh-Jim Dunn 《Applied Geophysics》 SCIE CSCD 2013年第4期397-410,511,共15页
The radial basis function (RBF) interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical prop... The radial basis function (RBF) interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman's RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart. 展开更多
关键词 Inverse problems radial basis function interpolation new approach
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Comparative Study of Radial Basis Functions for PDEs with Variable Coefficients
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作者 Fuzhang Wang Congcong Li Kehong Zheng 《Journal of Harbin Institute of Technology(New Series)》 CAS 2021年第6期91-96,共6页
The radial basis functions(RBFs)play an important role in the numerical simulation processes of partial differential equations.Since the radial basis functions are meshless algorithms,its approximation is easy to impl... The radial basis functions(RBFs)play an important role in the numerical simulation processes of partial differential equations.Since the radial basis functions are meshless algorithms,its approximation is easy to implement and mathematically simple.In this paper,the commonly⁃used multiquadric RBF,conical RBF,and Gaussian RBF were applied to solve boundary value problems which are governed by partial differential equations with variable coefficients.Numerical results were provided to show the good performance of the three RBFs as numerical tools for a wide range of problems.It is shown that the conical RBF numerical results were more stable than the other two radial basis functions.From the comparison of three commonly⁃used RBFs,one may obtain the best numerical solutions for boundary value problems. 展开更多
关键词 radial basis functions partial differential equations variable coefficient
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Performance of Compact Radial Basis Functions in the Direct Interpolation Boundary Element Method for Solving Potential Problems
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作者 C.F.Loeffle L.Zamprogno +1 位作者 W.J.Mansur A.Bulcao 《Computer Modeling in Engineering & Sciences》 2017年第3期367-387,共21页
This study evaluates the effectiveness of a new technique that transforms doma in integrals into boundary integrals that is applicable to the boundary element method.Si mulations were conducted in which two-dimensiona... This study evaluates the effectiveness of a new technique that transforms doma in integrals into boundary integrals that is applicable to the boundary element method.Si mulations were conducted in which two-dimensional surfaces were approximated by inter polation using radial basis functions with full and compact supports.Examples involving Poisson’s equation are presented using the boundary element method and the proposed te chnique with compact radial basis functions.The advantages and the disadvantages are e xamined through simulations.The effects of internal poles,the boundary mesh refinemen t and the value for the support of the radial basis functions on performance are assessed. 展开更多
关键词 Interpolations radial basis functions boundary element method Poisson’s equation
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