Parametric integral equations systems in 2D transient heat conduction analysis

Currently the most popular numerical methods used for solving transient heat conduction problems, finite element method (FEM) and boundary element method (BEM), have one fundamental defect – the necessity of discretizing the boundary or the domain. This problem escalates even more, when using an iterative process. 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. The purpose of this paper is to present PIES method for 2D transient heat conduction problems and present results obtained by solving few numerical examples. Accuracy and effectiveness of the method are shown in comparison with analytical solutions and FEM.