Automatic Construction of Phasefield Approximations from Sharp-Interface Models

The title says it all: this model uses a simple description of a sharp interface problem to derive a phasefield approximation which can then be solved using a finite-element toolbox. The domain specific language UFL is used both for defining the sharp interface model and for the weak formulation of the phasefield approximation. The resulting UFL form can then be inserted into any of the finite element packages available which can take UFL forms as an input. A class for evolving the solution over time is available based on dune and fenics. The bindings for the dune package include both local grid refinement and coarsening. This makes it easy to track the interface with a fine grid while a coarser grid can be used away from the interface. This is essential for evolving phasefield models efficiently. In addition the dune stepper also provides an efficient solver for obstacle problems so that double obstacle potentials can be used in the modelling. This solver is based on tnmg.

So far this model has been tested with:

• two phase models including additional bulk equations, e.g., for the temperature
• multphase models
• single phase models, e.g., crack propagation problems

Installation

The easiest way to test this module is using the docker container provided. Assuming docker is available on your system simply running the script rundune.sh will download the docker image for the dune-fem package and start the container. Within the container running the phasefield.sh script will complete the installation - this step takes some time but is only required the first time the docker container is set up. Within the docker container /host points to the folder from which rundune.sh was started, e.g., the root folder of this repository. Some examples are contained in the tutorials folder. More information on using the docker container can be found is available here including some information for MAC and Windows user.