A Meshless Boundary Element Method Formulation for Transient Heat Conduction Problems with Heat Sources


1 Department of Mechanical Engineering,Shiraz University

2 Department of Mechanical Engineering and Applied Mechanics,North Dakota State University


In the boundary element formulation of heat conduction, the heat source e ect imposes an
additional domain integral term on the system of integral equations. With this term, an
important advantage of the boundary element method as a boundary-only formulation will
be lost. This paper presents an accurate method for the evaluation of heat source domain
integrals, with no need of domain discretization. Transformation of the domain integral into the
corresponding boundary integral is carried out using Green's theorem. Both time-dependent and
time-independent fundamental solutions are considered. The methodology can be implemented
in general and for similar situations. Numerical examples will be presented to demonstrate the
accuracy and eciency of the presented method.