Parallel and GPU accelerated code for phase-field and reaction-diffusion simulations

TL;DR

SymPhas 2.0 is a comprehensive framework that enables symbolic, parallel, and GPU-accelerated simulations of phase-field and reaction-diffusion models, significantly boosting computational efficiency and scalability.

Contribution

It introduces symbolic differentiation, finite difference stencils, and GPU acceleration to SymPhas, enabling large-scale, high-performance simulations of complex models.

Findings

Achieved up to 1,000x speedup on large systems

Enabled direct model definition from free-energy functionals

Successfully integrated GPU computing with symbolic expressions

Abstract

We present SymPhas 2.0, a major update of the compile-time symbolic algebra simulation framework SymPhas for phase-field and reaction-diffusion models. This release introduces significant expansions and enhancements that enable the definition of a phase-field model directly from the free-energy functional via compile-time evaluated functional differentiation. It also introduces directional derivatives, symbolic summation, tensor-valued expressions, and compile-time derived finite difference stencils of arbitrary order and accuracy. Furthermore, the code has been parallelized for CPUs with MPI, and GPU computing has been added using CUDA (Compute Unified Device Architecture). For the latter, symbolic expressions are compiled into optimized CUDA kernels, allowing large-scale simulations to execute entirely on the GPU. For large systems ($32,768^2$ in 2D and $1,024^3$ in 3D with double precision), speedups up to $\sim \!\!1,000 \times$ were obtained compared to the first version of SymPhas using multi-threaded CPU execution on a single system. These developments establish SymPhas 2.0 as a flexible and scalable framework for efficient implementation of phase-field and reaction-diffusion models on GPU-based high-performance computing platforms.