The auxiliary boundary element method for time dependent problems

摘要

The boundary integral equation method or boundary element method is a well known technique to solve problems described by partial differential equations. By putting a source function on the boundary the partial differential equation is replaced by an equivalent integral equation defined on the boundary. Recently, some authors developped an alternative way by introducing an auxiliary boundary besides the physical boundary on which the source function is defined. Until now, this method has only been used for problems described by elliptic equations.In this contribution, it will be shown that the same idea can be used for parabolic equations. The technique has been applied to the diffusion equation. Experimental results have been obtained for a thermal diffusion problem including non linear boundary conditions. The experiments are also compared with the ‘classical’ boundary element method.