ParaPhase
Raum-Zeit-parallele adaptive Simulation von Phasenfeldmodellen auf Höchstleistungsrechnern

Phase-field models are an important class of mathematical techniques for the description of a multitude of industry-relevant physical and technical processes. Examples are the modelling of cracks and fracture propagation in solid media like ceramics or dry soil, the representation of liquid phase epitaxy for solar cells, semi-conductors or LEDs as well as melting and solidification processes of alloys.

The price for the broad applicability and mathematical elegance of this approach is the significant computing cost required for the simulation of phase-field equations at large scales. Solutions of these equations typically contain sharp interfaces moving through the domain. Such structures can only be resolved with carefully tuned, adaptive discretization schemes in space and time. Even worse, many key phenomena start to emerge only when the simulation domain is large and the simulation time is long enough. For example, in order to simulate micro cracks leading to fatigue failure of a piece of machinery, the domain must contain a certain number of these cracks. For epitaxy, in turn, structures are normally described on nano-scales, while the specimen sizes are on the order of centimeters. Thus, the enormous number of degrees-of-freedom for the discretization in space and time as well as the significant complexity of the simulation demand the use of modern HPC architectures.

The goal of the BMBF project “ParaPhase -- space-time parallel adaptive simulation of phase-field models on HPC architectures” is the development of algorithms and methods that allow for highly efficient space-time parallel and adaptive simulations of phase-field problems. Three key aspects will be addressed in the course of the project:

1. heterogeneous parallelization in space using an adaptive phase-field multigrid algorithm,
2. innovative parallelization in time and
3. high-order and flexible methods in space and time.

Based on the open source software DUNE, the “Distributed and Unified Numerics Environment”, the resulting algorithms will help to make large-scale HPC simulations accessible for researchers in these fields.