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

### Abstract

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 .

### Keywords

method of fundamental solutions; meshless method; radial basis functions; steady heat transfer, Poisson's equation; genetic algorithm; particular solution,### References

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**Computer Assisted Methods in Engineering and Science**, [S.l.], v. 15, n. 2, p. 99-112, july 2022. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/750>. Date accessed: 10 nov. 2024.