SymPhas—General Purpose Software for Phase‐Field, Phase‐Field Crystal, and Reaction‐Diffusion Simulations

Abstract

This work develops a new open source application programming interface (API) and software package called SymPhas for simulations of phase‐field, phase‐field crystal, and reaction‐diffusion models, supporting up to three dimensions and an arbitrary number of fields. SymPhas delivers two novel program capabilities: 1) User specification of models from the associated dynamical equations in an unconstrained form and 2) extensive support for integrating user‐developed discrete‐grid‐based numerical solvers into the API. The capability to specify general phase‐field models is primarily achieved by developing a novel symbolic algebra functionality that can formulate mathematical expressions at compile time; is able to apply rules of symbolic algebra such as distribution, factoring, and automatic simplification; and support user‐driven expression tree manipulation. A modular design based on the C++ template meta‐programming paradigm is applied to the symbolic algebra library and general API implementation to minimize application runtime and increase the accessibility of the API for third party development. SymPhas is written in C/C++ and emphasizes high‐performance capabilities via parallelization with OpenMP and the C++ standard library. SymPhas is equipped with a forward Euler solver and a semi‐implicit Fourier spectral solver. Sample implementations and simulations of several phase‐field models are presented, generated using the semi‐implicit Fourier spectral solver.

Computer Simulations of Deep Eutectic Solvents: Challenges, Solutions, and Perspectives

“…The PFM approach has been successful in a wide variety of application, such as directional solidification and dendritic growth [ 344 , 345 , 346 ], formation of polycrystalline structures [ 347 , 348 ], cardiac electric signals [ 349 , 350 ], and crystal growth [ 349 , 351 ] and electrochemical effects [ 352 ]. On the computational side, PFM is highly amenable to large-scale parallelizable simulations and there are a number of software packages available to simulate various phase-field models based on both finite element and finite difference methods that usually employ some level of parallelization [ 353 , 354 , 355 , 356 , 357 , 358 ].…”

Machine learning based data-driven discovery of nonlinear phase-field dynamics

“…The open-source SymPhas [26] software package was used to numerically simulate the above three systems. SymPhas allows the user to define phase-field models directly from their PDE formulations, and control simulation parameters from a single configuration file.…”

“…In each contour, = , = . The first contour shows U , the time derivative computed from the numerical solution generated by SymPhas [26], and the center contour shows U , the learned time derivative. The right panel shows the difference between U and U , as well as the corresponding rMSE value for each phase-field model.…”

“…We demonstrate the capability of the above algorithms to learn PDEs using data obtained from phase-field simulations of the well-known Allen-Cahn [22], Cahn-Hilliard [23], and the phase-field crystal (PFC) [24,25] models using the open source software SymPhas [26].…”

OpenPFC: an open-source framework for high performance 3D phase field crystal simulations

“…However, despite this progress, there remains a scarcity of open-source PFC codes accessible to researchers. One notable exception is SymPhas [18], which offers spectral solvers for phase field and PFC problems but is, at the time of writing this paper, limited to OpenMP-based shared memory parallelization, restricting computations to a single machine or node. Another noteworthy project is MEUMAPPS, a spectral solver designed for phase field modeling problems [19].…”