General Boundary Element Method for the Dual-Phase Lag Equations Describing the Heating of Two-Layered Thin Metal Films

  • Ewa MajchrzakEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 113)


Thermal interaction between two-layered thin metal film and the ultra-short laser pulse is considered. The problem is described by the system of the dual-phase lag equations supplemented by the appropriate boundary and initial conditions. To solve these equations the general boundary element method (GBEM) is proposed. At first, the GBEM for one layer is presented. Next, using the ideal contact condition at the interface between the layers (the form of this condition in the case of DPLE differs significantly from the classical condition occurring in the Fourier-type models), the final system of algebraic equations is formulated. At the stage of numerical computations the different intensities of the laser beam and the different exposure times are taken into account. The results are compared with the repeatedly verified explicit scheme of the finite difference method. The impact of the time step and length of internal cells on the results of computations is also discussed.


Dual-phase lag equation Thin metal films General boundary element method Ultra-short laser pulse 



The paper and research are financed within the project 2015/19/B/ST8/01101 sponsored by National Science Centre (Poland).


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Silesian University of TechnologyGliwicePoland

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