Spectral collocation methods for one-dimensional phase change problems with applications in laser processing of materials

Single and multi-domain spectral collocation methods utilizing Chebyshev polynomials were employed to obtain highly accurate solutions to one-dimensional phase change problems. The Landau transformation was imposed to fix the position of the moving boundary. Spatial derivatives were approximated using both spectral and finite-difference representations. Solutions to the resulting ordinary differential equations in time were obtained using the Gear and Adams predictor-corrector algorithms as implemented within the Mathematica programming environment. For test problems in which exact solutions were available the spectral representations were superior, in terms of computational efficiency and accuracy, to second-order-accurate finite-difference approximations. Solutions are also presented for the melting and vaporization of High Tc Y-Ba-Cu-O thin films under pulsed excimer laser irradiation