{'fraction_non_alphanumeric': 0.018619934282584884, 'fraction_numerical': 0.0032858707557502738, 'mean_word_length': 5.260273972602739, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
FINITE ELEMENT SOLUTION OF NON-FOURIER THERMAL WAVE PROBLEMS

A finite-element computational methodology is presented for the solution of transient non-Fourier heat conduction equations that describe the thermal wave propagation during the processing of thin films by ultrashort pulsing lasers. These problems are of hyperbolic type and possess both diffusion and wavelike behaviors. The problems are formulated within the framework of the Galerkin weighted residuals, and the Newmark time-stepping algorithm is used to carry out the time integration. The computer algorithm is validated using the analytical solution for 1-D thermal wave equations. Numerical simulations are made for 2-D and 3-D thermal wave propagations in single-phase media exposed to laser pulses. Incorporation of the method into the existing finite-element codes for structure analysis and/or for thermal fluids analysis is also discussed.