The software projects described below were developed as part of the accelerated finite element methods project.
libParanumal: library of parallel numerical algorithms for high-order finite element methods
The libParanumal library is an experimental test bed used to develop scalable multi-GPU finite element simulation tools. It was released on GitHub as an openly available research software project under the MIT license in 2018: https://github.com/paranumal/libparanumal
Resources: arXiv papers on GPU optimization of spectral element operations and a high-order discontinuous Galerkin based incompressible flow solver.
A collection of MATLAB scripts that accompany "Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications". Reference implementations include solvers for Maxwell's equations, elliptic equations, compressible Euler, compressible Navier-Stokes, and incompressible Navier-Stokes.
Previous software projects
PASIDG: GPU accelerated tsunami modeling
Goal: predict tsunami wave propagation using discontinuous Galerkin methods on triangular meshes using the two dimensional Shallow water equations. The method uses multirate Adams-Bashforth method for time integration, a positivity preserving method, and a slope limiter for stability of the numerical scheme. The implementations use OCCA for portability across several hardware architectures and multi-threading approaches.
Capabilities: reads GEBCO bathymetry data (link), GSHHS coastline data (link), gmsh meshing (link), interactive global region selection, multirate time-stepping, positivity preserving limiter, TVB limiting.
Hybridg: seismic inversion with discontinuous Galerkin methods
Description: a time-dependent linear acoustic-elastic water equation solver with RTM and FWI based imaging.
Capabilities: hybrid element meshes, multirate linear multistep local time-stepping, MPI+OCCA hybrid parallelism, acoustic/vti/tti/elastic modules, disk-free reverse time migration, consistent temporal correlation, time-reversed multirate time-stepping.