Parallelization of Phase-field Model for Phase Transformation Problem

This chapter focuses on parallelization of a 2D phase-field model for freezing into supercooled melt of a pure substance using OpenMP. The computational results presented here provide dendrite structures during their formation and evolution. The speedup factor displays a monotone increase with number of processors through 32. However, since the speedup increases only sub-linearly as the number of processors increase, it is clear that the parallel efficiency becomes quite low if more than 16 processors are employed. It introduces the equations of the phase-field model along with the scalings employed to render them dimensionless. Boundary and initial conditions required to formulate a well-posed mathematical problem are also prescribed. Parallelization of the numerical solution procedure is based on the shared-memory programming paradigm using the HP FORTRAN 90 HP-UX compiler. The program is parallelized using OpenMP running on the HP SuperDome at the University of Kentucky Computing Center. The chapter also introduces the phase-field model and briefly discusses numerical procedures and specific problem parameters. It then discusses the approach employed for parallelization, present computed results, and the speedups obtained.