An Efficient Numerical Procedure for Solving Microscale Heat Transport Equation During Femtosecond Laser Heating of Nanoscale Metal Films

An alternative discretization and solution procedure is developed for implicitly solving a microscale heat transport equation during femtosecond laser heating of nanoscale metal films. The proposed numerical technique directly solves a single partial differential equation, unlike other techniques available in the literature which split the equation into a system of two equations and then apply discretization. It is shown by von Neumann stability analysis that the proposed numerical method is unconditionally stable. The numerical technique is then extended to three space dimensions, and an overall procedure for computing the transient temperature distribution during short-pulse laser heating of thin metal films is presented. Douglas-Gunn time-splitting and delta-form Douglas-Gunn time-splitting methods are employed to solve the discretized 3-D equations; a simple argument for stability is given for the split equation. The performance of the proposed numerical scheme will be compared with the numerical techniques available in the literature and it is shown that the new formulation is comparably accurate and significantly more efficient. Finally, it is shown that numerical predictions agree with available experimental data during sub-picosecond laser heating.