A 3-D Cell Method Formulation for Coupled Electric and Thermal Problems

A finite formulation is presented for the solution of coupled problems of steady-state electric and transient thermal conductions in 3-D regions. The model is based on the cell method approach and takes advantage of the very agile algebraic formulations that it can provide for field theories. Dual barycentric cell complexes are used for both space and time domains, the latter inducing a Crank-Nicolson time integration scheme. An example of application is given, consisting in the simulation of a treatment for the thermal ablation of liver cancer. Comparisons are given with a commercial finite-element method program