نتایج جستجو برای: meshless collocation method

تعداد نتایج: 1632549  

Journal: :Applied Mathematics and Computation 2012
Hamou Sadat Cheng-An Wang Vital Le Dez

Keywords: Meshless method Coupled radiative–conductive transfer Discrete ordinates Even parity Complex geometries a b s t r a c t A meshless method DAM is employed to solve the coupled radiative and conductive heat transfer problem in a semi-transparent medium enclosed in complex 2D and 3D geome-tries. The meshless method for radiative transfer is based on the even parity formulation of the dis...

2008
Y. Duan S. J. Lai T. Z. Huang

This paper presents an efficient meshless approach for solving electrostatic problems. This novel approach is based on combination of radial basis functions-based meshless unsymmetric collocation method with projection domain decomposition method. Under this new method, we just need to solve a Steklov-Poincaré interface equation and the original problem is solved by computing a series of indepe...

2010
Shih-Wei Yang Yung-Ming Wang Chih-Ping Wu

A differential reproducing kernel (DRK) approximation-based collocation method is developed for solving ordinary and partial differential equations governing the oneand two-dimensional problems of elastic bodies, respectively. In the conventional reproducing kernel (RK) approximation, the shape functions for the derivatives of RK approximants are determined by directly differentiating the RK ap...

2011
G. Kosec B. Šarler

This paper introduces an effective H-adaptive upgrade to solution of the transport phenomena by the novel Local Radial Basis Function Collocation Method (LRBFCM). The transport variable is represented on overlapping 5-noded influence-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the variable are calculated from the ...

Journal: :SIAM J. Numerical Analysis 2008
Leevan Ling Robert Schaback

In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of E. Kansa’s well-known unsymmetric meshless collocation method. For a numerical implementation of the convergent variation, a previously proposed greedy technique is coupled with linear optimization. This algorithm allows a fully adaptive on-the-fly data-dependent m...

In this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. We approximate the exact solution by use of Radial Basis Function(RBF) collocation method. This techniqueplays an important role to reduce a fractional dierential equation to a system of equations. The numerical results demonstrate the accuracy and ability of this me...

2006
L. Ling R. Opfer R. Schaback

Though the technique introduced by E. Kansa [7, 8] is very successful in engineering applications, there were no proven results so far on the unsymmetric meshless collocation method for solving PDE boundary value problems in strong form. While the original method cannot be proven to be fail–safe in general, we prove asymptotic feasibility for a generalized variant using separated trial and test...

2007

Over the past two decades meshless methods have attracted much attention owing to their advantages in adaptivity, higher degree of solution field continuity, and capability to handle moving boundary and changing geometry. In this work, a meshless integral method based on the regularized boundary integral equation has been developed and applied to two-dimensional linear elasticity and elastoplas...

Journal: :SIAM J. Numerical Analysis 2007
Peter Giesl Holger Wendland

In this paper, we derive error estimates for generalized interpolation, in particular collocation, in Sobolev spaces. We employ our estimates to collocation problems using radial basis functions and extend and improve previously known results for elliptic problems. Finally, we use meshless collocation to approximate Lyapunov functions for dynamical systems.

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