M.Sc. Public Lecture (Math) - Steven Silber

"SymPhas: A modular API for phase-field modeling using compile-time symbolic algebra"

Phase-field modelling is a common approach to studying phase transitions; it provides a framework for describing the physical process of a phase transition through a set of dynamical equations to visualize the complex mechanisms that take place, vital in diverse applications from steel-forming to cardiac modelling. To address the limited software packages available for phase-field modelling, a new open source API and software package called SymPhas is developed for simulating general phase-field models in 1-, 2- and 3-dimensions, including those specified by multiple dynamical equations. SymPhas implements multiple numerical solvers and allows user-developed solvers as well. This is accomplished using a novel approach that allows a mathematical expression to be transformed and manipulated in the compilation stage when the code is built into the runnable program. This functionality is used by an algorithm, specific to each numerical solver, which transforms a set of dynamical equations for an arbitrary phase-field model into an object that the solver uses to determine the phase transition evolution. The functional components of SymPhas are separated in a modular way, maximizing program robustness and enhancing community development potential. Several test cases of different phase transition types, including one that involves two dynamical equations, are developed. The test cases are also presented with the respective implementations in SymPhas. SymPhas is written in C/C++ and has been tested in Linux and Windows environments.