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UDC 519.6
D.O. Protektor1, V.M. Kolodyazhny2, D.O. Lisin3, O.Yu. Lisina4


1 V.N. Karazin Kharkiv National University, Kharkiv, Ukraine

 d.protector@karazin.ua

2 Kharkiv National Automobile and Highway University, Kharkiv, Ukraine

 vladmax1949@ukr.net

3 V.N. Karazin Kharkiv National University, Kharkiv, Ukraine

 d.lisin@karazin.ua

4 V.N. Karazin Kharkiv National University, Kharkiv, Ukraine

 o.lisina@karazin.ua

A MESHLESS METHOD FOR SOLVING THREE-DIMENSIONAL
NONSTATIONARY HEAT CONDUCTION PROBLEMS IN ANISOTROPIC MATERIALS

Abstract. The article deals with a meshless method for solving three-dimensional nonstationary heat conduction problems in anisotropic materials. A combination of dual reciprocity method using anisotropic radial basis function and method of fundamental solutions is used to solve the boundary-value problem. The method of fundamental solutions is used for obtain the homogenous part of the solution; the dual reciprocity method with the use of anisotropic radial basis functions allows obtaining a partial solution. The article shows the results of numerical solutions of two benchmark problems obtained by the developed numerical method; average relative, average absolute, and maximum errors are calculated.

Keywords: meshless method, boundary-value problems, anisotropic materials, dual reciprocity method, method of fundamental solution, anisotropic radial basis functions.



FULL TEXT

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