PT diffusion - MWE

Simple multi-xPU diffusion solvers to showcase itertive accelerated solvers.

This repository contains a set of 2D explicit and iterative implicit diffusion solvers to run on xPU (CPU or GPU) using ParallelStencil.jl; the multi-xPU version uses ImplicitGlobalGrid.jl.

The scripts in this repo solve the time-dependent diffusion equation with variable coefficient:

qT        = -λ ∇ T
ρCp dT/dt = -∇ ⋅ qT

using an explicit approach (diffusion_2D_expl_xpu.jl) or an iterative implicit approach (diffusion_2D_impl_xpu.jl) based on the pseudo-transient acceleration.

The multi-xPU code (diffusion_2D_expl_mxpu.jl) allows to run the explicit diffusion example on multiple CPUs and GPUs using distributed memory parallelisation.

Further information on the accelerated pseudo-transient method can be found in the Räss et al. 2022 GMD discussion paper, extending the original idea from Frankel (1950).

Other usefull resources can be found here:

• https://github.com/PTsolvers/PseudoTransientDiffusion.jl
• https://pde-on-gpu.vaw.ethz.ch/lecture4/