Towards a Three-Dimensional Parallel, Adaptive, Multilevel Solver for the Solution of Nonlinear, Time-Dependent, Phase-Change Problems

摘要: One of the fundamental open challenges that computational engineering practitioners continue to face is combining modern numerical algorithms, such as mesh adaptivity and efficient multilevel solvers, with a parallel implementation permits scalable performance on large numbers cores. The problems must be overcome include need maintain an effective load balance responds dynamically local refinement and/or coarsening, difficulty obtaining good efficiencies for those operations take place at coarsest levels solver. In this paper we report our ongoing research which seeks make progress towards resolving some these through application parallel, adaptive, approach solution highly challenging class phase-change involving very wide range length time scales. mathematical models seek solve form systems nonlinear, stiff, parabolic partial differential equations (PDEs) in three space dimensions. solutions PDEs require extremely high spatial resolution near moving interface so essential. Furthermore, stiffness implies implicit time-stepping used resulting nonlinear algebraic are solved using multigrid locally refined meshes. In first part provide details study, including their formulation, illustrate both adaptive fully time-stepping, even just two desire move dimensions provides primary motivation extending techniques architectures, forms substance second half paper. We introduce source software tool, PARAMESH [1], describe how have developed it allow its problems, use adaptively meshed dimensions, parallel. Initially simple linear model order begin assess software, followed by results computed PDE typical rapid solidification problem. concludes summary short description planned future work.