Transient heat conduction analysis in a piecewise homogeneous domain by a coupled boundary and finite element method

A coupled finite element-boundary element analysis method for the solution of transient two-dimensional heat conduction equations involving dissimilar materials and geometric discontinuities is developed. Along the interfaces between different material regions of the domain, temperature continuity and energy balance are enforced directly. Also, a special algorithm is implemented in the boundary element method (BEM) to treat the existence of corners of arbitrary angles along the boundary of the domain. Unknown interface fluxes are expressed in terms of unknown interface temperatures by using the boundary element method for each material region of the domain. Energy balance and temperature continuity are used for the solution of unknown interface temperatures leading to a complete set of boundary conditions in each region, thus allowing the solution of the remaining unknown boundary quantities. The concepts developed for the BEM formulation of a domain with dissimilar regions is employed in the finite element-boundary element coupling procedure. Along the common boundaries of FEM-BEM regions, fluxes from specific BEM regions are expressed in terms of common boundary (interface) temperatures, then integrated and lumped at the nodal points of the common FEM-BEM boundary so that they are treated as boundary conditions in the analysis of finite element method (FEM) regions along the common FEM-BEM boundary.