A comparison of two SGBEM solutions of an unsteady heat conduction interface problem

A comparison of two approaches for solving time dependence in an unsteady heat conduction problem with a material or other interface, based on a boundary element technique is presented. A quadrature algorithm is used in the first approach for calculating convolutional integrals, which leads directly to the time-domain solution of the problem; the other approach uses the Laplace transform and a numerical inversion of the Laplace domain solution. The new numerical techniques lead together with the Symmetric Galerkin Boundary Element Method applied for space variables and a weak formulation of interface conditions to an interface problem with generally curved interfaces and to independent meshing of each side of the interface. The discussion on numerical results is focused on the non-matching discretization of the interface. The obtained data are also compared with known analytical solutions, if available, and discussed in the cases of different material properties pertinent to substructures on both sides of the interface.