Title: The Three M’s of Scientific Computing: A High-Performance Solution to the FCH Equation
Abstract: Modern computing architecture is advancing our ability to approximate solutions to partial differential equations. I will present an example of how a graphics processing unit (GPU) can make a large problem tractable. The Functionalized Cahn-Hilliard (FCH) equation in three dimensions,
ut = Δ(ε2Δ – W″(u) + ε2η)(ε2 Δu – W′(u)),
describes pore network formation in a functionalized polymer/solvent system like those used in hydrogen fuel cells. The physical process is defined by multiple time-scales: short time phase separation, long time network growth, and slow evolution to steady state. This requires very long, accurate simulations to correctly describe the physics. I will present a fast, numerically stable, and time-accurate method for solving the FCH equation. Experimentation with several different methods for computing time evolution led to a Fourier spectral method in space with an exponential time integrator giving the desired qualities. Numerical results on a GPU show a 10x speedup over a fully-parallelized eight-core CPU.