A hybrid time/Laplace integration method based on numerical Green’s functions in conduction heat transfer

The present paper describes an efficient time/Laplace domain approach to analyze numerically heat conduction problems. An efficient recurrence relationship for the temperature in the time-domain, based on the Green’s functions of the model, is presented. Primarily, Green’s functions in nodal coordinates are explicitly calculated by the finite element method in the Laplace domain and subsequently, the Stehfest and the Zakian Laplace inversion schemes are employed to compute numerically Green’s functions that transfer solution at time 0 to time Δt. As a result, a new family of highly accurate time integration methods called ExGA-Stehfest and ExGA-Zakian is obtained. Finally, numerical examples are presented in order to illustrate the high accuracy and potentialities of these novel approaches.