MODERN METHODS OF MATHEMATICAL MODELING IN LASER MATERIAL PROCESSING TECHNOLOGIES

Silantev Danila Mikhailovich

The article presents a systematic analysis of current research in the field of laser material processing with an emphasis on the mathematical models employed. Various classes of computational methods are reviewed, including transient heat transfer models based on the unsteady heat conduction equation, finite element modeling (COMSOL, ANSYS), multiscale approaches (DFT, molecular mechanics), statistical experimental design methods, and models of plasmonic effects and nonlinear optics. Special attention is paid to hybrid computational schemes that combine different physical approaches. The effectiveness of mathematical modeling for predicting laser processing outcomes and optimizing technological parameters is demonstrated.

Keywords:laser processing of materials, mathematical modeling, heat conduction equation, finite element analysis, DFT modeling, plasmonic effects, nonlinear optics, digital twins, multiscale modeling, optimization of technological processes.