SC19 Proceedings

The International Conference for High Performance Computing, Networking, Storage, and Analysis

Poster 149: Solving Phase-Field Equations in Space-Time: Adaptive Space-Time Meshes and Stabilized Variational Formulations

Authors: Kumar Saurabh (Iowa State University), Biswajit Khara (Iowa State University), Milinda Fernando (University of Utah), Masado Ishii (University of Utah), Hari Sundar (University of Utah), Baskar Ganapathysubramanian (Iowa State University)

Abstract: We seek to efficiently solve a generalized class of partial differential equations called the phase-field equations. These non-linear PDE’s model phase transition (solidification, melting, phase-separation) phenomena which exhibit spatially and temporally localized regions of steep gradients. We consider time as an additional dimension and simultaneously solve for the unknown in large blocks of time (i.e. in space-time), instead of the standard approach of sequential time-stepping. We use variational multiscale (VMS) based finite element approach to solve the ensuing space-time equations. This allows us to (a) exploit parallelism not only in space but also in time, (b) gain high order accuracy in time, and (c) exploit adaptive refinement approaches to locally refine region of interest in both space and time. We illustrate this approach with several canonical problems including melting and solidification of complex snow flake structures.

Best Poster Finalist (BP): no

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