Trigonometric variable shape parameter and exponent strategy for generalized multiquadric radial basis function approximation

被引：40

作者：

Xiang, Song ^{[1
]}

Wang, Ke-ming ^{[1
]}

Ai, Yan-ting ^{[1
]}

Sha, Yun-dong ^{[1
]}

Shi, Hong ^{[1
]}

机构：

[1] Shenyang Aerosp Univ, Sch Engine & Energy Engn, Shenyang 110136, Peoples R China

来源：

APPLIED MATHEMATICAL MODELLING | 2012年 / 36卷 / 05期

关键词：

Trigonometric variable shape parameter; Generalized multiquadric; Radial basis function; Interpolation; Linear boundary value problem; PARTIAL-DIFFERENTIAL-EQUATIONS; COMPUTATIONAL FLUID-DYNAMICS; INTERPOLATION; SCHEME;

D O I：

10.1016/j.apm.2011.07.076

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The generalized multiquadric radial basis function (phi(j) = [(x - x(j))(2) + c(2)](beta)) has the exponent beta and shape parameter c that play an important role in the accuracy of he approximation. In this study, we present a trigonometric variable shape parameter and exponent strategy and apply it to function interpolations and linear boundary value problems. Several numerical experiments with the uniformly spaced nodes show that the inverse multiquadric radial basis function (beta = -0.5) with the trigonometric variable shape parameter c strategy results in the best accuracy for the one-dimensional interpolations; the trigonometric variable shape parameters and exponent strategy produces the best accuracy for the two-dimensional interpolations and linear boundary value problems. For the non-uniformly spaced nodes, the random variable shape parameter c and exponent beta strategy produces the best accuracy for the two-dimensional boundary value problem. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1931 / 1938

页数：8

共 12 条

[1] THE PARAMETER R2 IN MULTIQUADRIC INTERPOLATION [J].

CARLSON, RE ;

FOLEY, TA .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1991, 21 (09) :29-42

[2] Exponential convergence and H-c multiquadric collocation method for partial differential equations [J].

Cheng, AHD ;

Golberg, MA ;

Kansa, EJ ;

Zammito, G .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2003, 19 (05) :571-594

[3] Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter [J].

Ferreira, A. J. M. ;

Fasshauer, G. E. ;

Batra, R. C. ;

Rodrigues, J. D. .

COMPOSITE STRUCTURES, 2008, 86 (04) :328-343

[4] Numerical simulation of two-dimensional combustion using mesh-free methods [J].

Kansa, Edward J. ;

Aldredge, Ralph C. ;

Ling, Leevan .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2009, 33 (07) :940-950

[5] MULTIQUADRICS - A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS .1. [J].

KANSA, EJ .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1990, 19 (8-9) :127-145

[6] MULTIQUADRICS - A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS .2. SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL-DIFFERENTIAL EQUATIONS [J].

KANSA, EJ .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1990, 19 (8-9) :147-161

[7] Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations [J].

Kansa, EJ ;

Hon, YC .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2000, 39 (7-8) :123-137

[8] An algorithm for selecting a good value for the parameter c in radial basis function interpolation [J].

Rippa, S .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 1999, 11 (2-3) :193-210

[9] A random variable shape parameter strategy for radial basis function approximation methods [J].

Sarra, Scott A. ;

Sturgill, Derek .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2009, 33 (11) :1239-1245

[10] Parameter optimization in multiquadric response surface approximations [J].

Wang, BP .

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, 2004, 26 (3-4) :219-223

← 1 2 →