Matlab tools for HDG in three dimensions

TL;DR

This paper introduces Matlab tools for efficient, modular, and parallelized implementation of Hybridizable Discontinuous Galerkin methods for 3D reaction-diffusion and convection-diffusion problems, including superconvergent postprocessing.

Contribution

It provides a set of Matlab tools that are optimized for vectorized, parallelized computation of HDG methods in three dimensions, with added features for convection-diffusion and superconvergence.

Findings

Tools enable efficient vectorized coding of HDG in 3D

Parallelization improves computational performance

Includes superconvergent postprocessing techniques

Abstract

In this paper we provide some Matlab tools for efficient vectorized coding of the Hybridizable Discontinuous Galerkin for linear variable coefficient reaction-diffusion problems in polyhedral domains. The resulting tools are modular and include enhanced structures to deal with convection-diffusion problems, plus several projections and a superconvergent postprocess of the solution. Loops over the elements are exclusively local and, as such, have been parallelized.