A meshless method for solving three-dimensional nonstationary heat conduction problems in anisotropic materials / Protektor, / Kolodyazhny, / Lisin, / Lisina. (2021)
Ukrainian

English  Cybernetics and Systems Analysis   /     Issue (2021, 57 (3))

Protektor D.O., Kolodyazhny V.M., Lisin D.O., Lisina O.Y.
A meshless method for solving three-dimensional nonstationary heat conduction problems in anisotropic materials

The authors describe 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 to 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. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: anisotropic materials, anisotropic radial basis functions, boundary-value problems, dual reciprocity method, meshless method, method of fundamental solution, Boundary value problems, Functions, Image segmentation, Numerical methods, Optical anisotropy, Anisotropic material, Bench-mark problems, Dual reciprocity methods, Mesh-less methods, Method of fundamental solutions, Nonstationary heat conduction, Numerical solution, Radial basis functions, Heat conduction


Cite:
Protektor D.O., Kolodyazhny V.M., Lisin D.O., Lisina O.Y. (2021). A meshless method for solving three-dimensional nonstationary heat conduction problems in anisotropic materials. Cybernetics and Systems Analysis, 57 (3), 152–163. doi: https://doi.org/10.1007/s10559-021-00372-8 http://jnas.nbuv.gov.ua/article/UJRN-0001239417 [In Ukrainian].


 

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