Integrating Odeint Time Stepping into OpenFPM for Distributed and GPU Accelerated Numerical Solvers

We present a software implementation integrating the time-integration library Odeint from Boost with the OpenFPM framework for scalable scientific computing. This enables compact and scalable codes for multi-stage, multi-step, and adaptive explicit time integration on distributed-memory parallel computers and on Graphics Processing Units (GPUs). The present implementation is based on extending OpenFPM's metaprogramming system to Odeint data types. This makes the time-integration methods from Odeint available in a concise template-expression language for numerical simulations distributed and parallelized using OpenFPM. We benchmark the present software for exponential and sigmoidal dynamics and present application examples to the 3D Gray-Scott reaction-diffusion problem and the "dam break" problem from fluid mechanics. We find a strong-scaling efficiency of 80% on up to 512 CPU cores and a five-fold speedup on a single GPU.