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

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

Non-element method of solving 2D boundary problems defined on polygonal domains modeled by Navier equation

AbstractThe paper presents a non-element method of solving boundary problems defined on polygonal domains modeled by corner points. To solve these problems a parametric integral equation system (PIES) is used. The system is characterized by a separation of the approximation of boundary geometry from the approximation of boundary functions. This feature makes it possible to effectively investigate the convergence of the obtained solutions with no need of performing the approximation of boundary geometry. The testing examples included confirm high accuracy of the solutions

The effective strategy for calculating strains and stresses in elasto-plastic torsion of a bar

The paper presents the general approximation strategy for derivatives of solutions obtained by the parametric integral equation system (PIES). The proposed approach is applied to calculating derivatives in linear and nonlinear torsion of a bar. The nonlinear problem is solved iteratively and requires repeated calculating of integrals in order to determine stresses or strains. Due to elimination of the repeated integration, the proposed strategy increases the efficiency of calculations. Furthermore, it ensures high accuracy of solutions to the considered problem, which has been tested in comparison to the analytical and/or numerical solutions reported in the literature obtained by other methods