Accelerated Simulation of Surface Pattern-Forming Systems Via Hierarchical Multi-Scale and Mesoscopic Modeling

Recent advances in the development of mesoscopic models have opened new avenues for hierarchical multi-scale modeling and simulation of materials with nano-scale features. Using a consistent microscopic model as a basis, fine-grained stochastic (kinetic Monte Carlo) and coarse-grained deterministic (mesoscopic continuum) can be cooperatively applied to prototyping and optimization of bottom-up manufacturing of these materials. A fundamental challenge to these simulation techniques is the difficulty in their parallelization.

Mesoscopic models typically involve integro-partial differential equations due to the presence of global interactions terms. This motivates the use of (Fourier) spectral methods, for which we present an accelerated computational framework. This framework leverages existing optimized numerical libraries for discrete Fourier transform computation and implicit integration. In addition, cutting-edge GPU-acceleration techniques are shown to be advantageous depending on system size. Finally, a novel application of a Newton-Krylov nonlinear solver is shown to enable some degree of parallelization of the spectral method through distributed computation in the preconditioning stage.