Presentation

DescriptionWe 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.