A stable three-level finite difference scheme for solving the parabolic two-step model in a 3D micro-sphere heated by ultrashort-pulsed lasers

  • Authors:

  • Ibrahima K. Kaba;Weizhong Dai

  • Affiliations:

  • Mathematics & Statistics, College of Engineering & Science, Louisiana Tech University, Ruston, LA;Mathematics & Statistics, College of Engineering & Science, Louisiana Tech University, Ruston, LA

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2005

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Abstract

Ultrashort-pulsed lasers with pulse durations of the order of sub-picosecond to femtosecond domain possess exclusive capabilities in limiting the undesirable spread of the thermal process zone in the heated sample. Parabolic two-step micro heat transport equations have been widely applied for thermal analysis of thin metal films exposed to picosecond thermal pulses. In this study, we develop a three level finite difference scheme for solving the heat transport equations in a three-dimensional micro-sphere heated by ultrashort-pulsed lasers. It is shown that the scheme is unconditionally stable. The method is illustrated by numerical examples.