The Explicit Green's Approach with stability enhancement for solving the bioheat transfer equation

The aim of this paper is to propose a strategy for performing a stability enhancement into the Explicit Green's Approach (ExGA) method applied to the bioheat transfer equation. The ExGA method is a time-stepping technique that uses numerical Green's functions in the time domain; these functions are here computed by the FEM. Basically, a new two nonequal time substeps procedure is proposed to compute Green's functions at the first time step. This is accomplished by adopting the standard explicit Euler scheme and an optimized procedure to yield the best stability constraint, allowing a reduction into the number of time steps without loss of accuracy. In addition, the concept of local numerical Green's functions is introduced and explored aiming at reducing the computational effort of nodal Green's functions calculation. Two examples are presented in order to show the potentialities of the proposed methodology, one to illustrate the accuracy and another applied to skin burn simulations.