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Optimal parameters of method of fundamental solutions for Poisson problems in heat transfer by means of genetic algorithms

Kołodziej J. A., Klekiel T.

Computer Assisted Mechanics and Engineering Sciences

2008

Vol. 15, No. 2

99-112

This paper describes the application of the method of fundamental solutions to the solution of the boundary value problems of the two-dimensional steady heat transfer with heat sources. For interpolation of an inhomogeneous term in Poisson equation the radial basis functions are used. Three cases of boundary value problems are solved and five cases of radial basis functions are used. For comparison purposes the boundary value problems for which exact solution exists were chosen. Application of method of fundamental solutions with boundary collocation and radial basis function for solution of inhomogeneous boundary value problems introduces some number of parameters related with these tools. For optimal choosing of these parameters the genetic algorithm is used. The results of numerical experiences related to optimal parameters are presented.

Boundary element method in the inverse problems of steady heat transfer

Majchrzak E., Freus K.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2003

Vol. 2, nr 1

77--86

The methods of inverse problems solution appearing in the domain of steady heat transfer are discussed. In particular, the inverse boundary problems (the identification of the boundary values on the part of the surface limiting the system analyzed) and the inverse parametric problems (reconstruction of the thermophysical parameters of the material) are considered. Such problems have been solved using (on the stage of numerical computations) the boundary element method. The different methods of inverse problems solution have been applied. So, the direct method, the least squares method in the basic version, the same method supplemented by the regularization terms, the method of the energy minimization and also the algorithm basing on the sensitivity coefficients have been taken into account. The computations can been realized for different numbers and positions of the control points, the possible disturbances of 'measured' temperatures have been also taken into account. The remarks concerning the exactness and effectiveness of successive methods of the inverse problem solution have been formulated. The theoretical considerations are supplemented by the examples of computations verifying the correctness of the algorithms proposed. by the examples of computations verifying the correctness of the algorithms proposed.