Some recent results and proposals for the use of radial basis functions in the BEM

Golberg, Michael A.; Chen, C.S.; Bowman, H.

doi:10.1016/s0955-7997(98)00087-3

Cited by 276 publications

(98 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The numerical analysis of heat transfer [10][11][12][13][14] has been independently, though not exclusively, developed in four main streams: the finite difference method (FDM) [15,16], the finite volume method (FVM) [17], the finite element method (FEM) [18][19][20], and the boundary element method (BEM) [21][22][23]. The FDM is based on using Taylor series expansion to find approximation formulas for derivative operators.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Simulation of the Laminar Forced Convective Heat Transfer between Two Concentric Cylinders

Sârbu

Iosif

2017

Computation

View full text Add to dashboard Cite

Abstract:The dual reciprocity method (DRM) is a highly efficient numerical method of transforming domain integrals arising from the non-homogeneous term of the Poisson equation into equivalent boundary integrals. In this paper, the velocity and temperature fields of laminar forced heat convection in a concentric annular tube, with constant heat flux boundary conditions, have been studied using numerical simulations. The DRM has been used to solve the governing equation, which is expressed in the form of a Poisson equation. A test problem is employed to verify the DRM solutions with different boundary element discretizations and numbers of internal points. The results of the numerical simulations are discussed and compared with exact analytical solutions. Good agreement between the numerical results and exact solutions is evident, as the maximum relative errors are less than 5% to 6%, and the R 2 -values are greater than 0.999 in all cases. These results confirm the effectiveness and accuracy of the proposed numerical model, which is based on the DRM.

show abstract

Section: Introductionmentioning

confidence: 99%

“…Unlike the FEM, which requires that the domain be meshed, the BEM only discretizes the boundary. Therefore, the amount of data necessary for solving a problem can be greatly reduced [21][22][23][24]. A complete review of the BEM's domain integrals is presented in [25].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of the Laminar Forced Convective Heat Transfer between Two Concentric Cylinders

Sârbu

Iosif

2017

Computation

View full text Add to dashboard Cite

show abstract

“…They have pointed out that the omission of the linear terms could have biased the numerical results. They also showed that a full understanding of convergence behavior of the DRM requires one to consider both interpolation and BEM errors [115], since the later can o set the e ect of data approximation [116]. Karur et al [117] have used DRM in their work.…”

Section: Rbfns In Approximation and Interpolationmentioning

confidence: 99%

Radial basis function neural networks: a topical state-of-the-art survey

Dash¹,

Behera²,

Dehuri

et al. 2016

Open Computer Science

View full text Add to dashboard Cite

Radial basis function networks (RBFNs) have gained widespread appeal amongst researchers and have shown good performance in a variety of application domains. They have potential for hybridization and demonstrate some interesting emergent behaviors. This paper aims to o er a compendious and sensible survey on RBF networks. The advantages they o er, such as fast training and global approximation capability with local responses, are attracting many researchers to use them in diversi ed elds. The overall algorithmic development of RBF networks by giving special focus on their learning methods, novel kernels, and ne tuning of kernel parameters have been discussed. In addition, we have considered the recent research work on optimization of multi-criterions in RBF networks and a range of indicative application areas along with some open source RBFN tools.

show abstract

“…A sufficient condition for the interpolation matrix to be invertible is that the basis functions is positive definite on . Unfortunately, not all globally supported RBFs satisfy this condition, thus some polynomials should generally be added to (2) for a mathematically consistent implementation [14], although the interpolation form of (2) is commonly used by fellow researchers in the computational electromagnetics community.…”

Section: A Radial Basis Function Interpolationmentioning

confidence: 99%

“…It follows naturally that (14) This approach allows one to choose a relatively large scale at the lowest level to capture the overall behavior of the function, and by decreasing it during the process of the procedure, finer and finer details of the function is obtained step by step, providing a hierarchical construction procedure with an acceptable computing time. In other words, this approach allows one to adjust the support of the CS-RBFs according to the point density, with a reasonable tradeoff between interpolation efficiency and accuracy, that would still result in an improvement in the interpolation quality.…”

Section: A Cluster Algorithm To Decompose the Sample Points Into Amentioning

confidence: 99%

A response surface methodology based on improved compactly supported radial basis function and its application to rapid optimizations of electromagnetic devices

Yang²,

et al. 2005

IEEE Trans. Magn.

View full text Add to dashboard Cite

The compactly supported radial basis function (CS-RBF) is improved and used to design a new response surface model. The model is incorporated into stochastic global optimal methods to develop a fast and efficient global optimal design strategy with the main target to reduce the number of function calls that involve computationally heavy procedures such as, for example, the repetitive usage of finite element analysis which is generally required in solving inverse problems. In order to employ a multistep method to automatically adjust the support of the CS-RBF to realize the "best" tradeoff between computational efficiency and accuracy, a cluster algorithm is proposed to decompose the sample points into a nested sequence of subsets. To validate the proposed algorithm, typical numerical results on two different examples are reported.Index Terms-Compact support, optimal design, radial basis function, response surface methodology.

show abstract

Some recent results and proposals for the use of radial basis functions in the BEM

Cited by 276 publications

References 40 publications

Numerical Simulation of the Laminar Forced Convective Heat Transfer between Two Concentric Cylinders

Numerical Simulation of the Laminar Forced Convective Heat Transfer between Two Concentric Cylinders

Radial basis function neural networks: a topical state-of-the-art survey

A response surface methodology based on improved compactly supported radial basis function and its application to rapid optimizations of electromagnetic devices

Contact Info

Product

Resources

About