Vol. 3, No. 6, 2008

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The optimal shape parameter of multiquadric collocation method for solution of nonlinear steady-state heat conduction in multilayered plate

Jan Adam Kołodziej and Magdalena Mierzwiczak

Vol. 3 (2008), No. 6, 1077–1086

This paper deals with the numerical solution of the nonlinear heat transfer problem in a multilayered plate. Kansa’s meshless method is used for the solution of this problem. In this approach, the unknown temperatures in layers are approximated by the linear combination of radial basis functions, while the governing equation and the boundary conditions are imposed directly at the collocation points. The multiquadrics [MQ] are used as the radial basis functions. In the presented method the radial basis functions contains a free parameter C, called the shape parameter. Usually, in the application of radial basis functions, this parameter is chosen arbitrarily depending on the author’s experience. In the presented paper, special attention is paid to the optimal choice of the shape parameter for the radial basis functions. This optimal value of the shape parameter is obtained using a formula given by other authors for solution of the linear case.

meshless method, heat transfer, Kansa's method, temperature-dependent thermal conductivity, optimal shape parameter, residual error
Received: 7 February 2008
Revised: 26 April 2008
Accepted: 26 April 2008
Published: 1 August 2008
Jan Adam Kołodziej
Institute of Applied Mechanics
Poznan University of Technology
ul. Piotrowo 3
60-965 Poznan
Magdalena Mierzwiczak
Institute of Applied Mechanics
Poznan University of Technology
ul. Piotrowo 3
60-965 Poznan