<abstract xmlns="http://www.w3.org/1999/xhtml"><p>One of the most popular applications of high power lasers is heating of the surface layer of a material, in order to change its properties. Numerical methods allow an easy and fast way to simulate the heating process inside of the material. The most popular numerical methods FEM and BEM, used to simulate this kind of processes have one fundamental defect, which is the necessity of discretization of the boundary or the domain. An alternative to avoid the mentioned problem are parametric integral equations systems (PIES), which do not require classical discretization of the boundary and the domain while being numerically solved. PIES method was previously used with success to solve steady-state problems, as well as transient heat transfer problems. The purpose of this paper is to test the efficacy of the PIES method with time discretization in solving problem of laser heating of a material, with different pulse shape approximation functions.</p></abstract>

One of the most popular applications of high power lasers is heating of the surface layer of a material, in order to change its properties. Numerical methods allow an easy and fast way to simulate the heating process inside of the material. The most popular numerical methods FEM and BEM, used to simulate this kind of processes have one fundamental defect, which is the necessity of discretization of the boundary or the domain. An alternative to avoid the mentioned problem are parametric integral equations systems (PIES), which do not require classical discretization of the boundary and the domain while being numerically solved. PIES method was previously used with success to solve steady-state problems, as well as transient heat transfer problems. The purpose of this paper is to test the efficacy of the PIES method with time discretization in solving problem of laser heating of a material, with different pulse shape approximation functions.

Parametric Integral Equations Systems Method In Solving Unsteady Heat Transfer Problems For Laser Heated Materials

Faculty of Mechanical Engineering, Bialystok University of Technology, ul. Wiejska 45C, 15-351 Białystok, Poland

Faculty of Mathematics and Computer Science, University of Bialystok, ul. Konstantego Ciołkowskiego 1M, 15-245 Białystok

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

One of the most popular applications of high power lasers is heating of the surface layer of a material, in order to change its properties. Numerical methods...

Parametric Integral Equations Systems Method In Solving Unsteady Heat Transfer Problems For Laser Heated Materials

Published Online: Nov 07, 2015

Page range: 167 - 172

Received: Apr 11, 2015

Accepted: Oct 28, 2015

DOI: https://doi.org/10.1515/ama-2015-0028

Keywords
PIES Method, Transient Heat Transfer, Laser Heating, FEM

© 2015 Bialystok University of Technology

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Parametric Integral Equations Systems Method In Solving Unsteady Heat Transfer Problems For Laser Heated Materials

Published Online: Nov 07, 2015

Page range: 167 - 172

Received: Apr 11, 2015

Accepted: Oct 28, 2015

DOI: https://doi.org/10.1515/ama-2015-0028

KeywordsPIES Method, Transient Heat Transfer, Laser Heating, FEM

© 2015 Bialystok University of Technology

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
PIES Method, Transient Heat Transfer, Laser Heating, FEM