HDGlab: An open-source implementation of the hybridisable discontinuous Galerkin method in MATLAB

TL;DR

HDGlab is an open-source MATLAB tool that implements the hybridisable discontinuous Galerkin method, supporting high-order polynomials, curved elements, and adaptive strategies to enhance computational engineering applications.

Contribution

It provides a detailed, accessible implementation of the HDG method with features like high-order polynomials, curved elements, and mesh integration, not available in other open-source codes.

Findings

Supports polynomial degrees up to nine with various nodal distributions.

Enables curved isoparametric elements in 2D and 3D.

Facilitates practical applications through Gmsh integration.

Abstract

This paper presents HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation available in HDGlab. Ultimately, this is expected to make this relatively new advanced discretisation method more accessible to the computational engineering community. HDGlab presents some features not available in other implementations of the HDG method that can be found in the free domain. First, it implements high-order polynomial shape functions up to degree nine, with both equally-spaced and Fekete nodal distributions. Second, it supports curved isoparametric simplicial elements in two and three dimensions. Third, it supports non-uniform degree polynomial approximations and it provides a flexible structure to devise degree adaptivity strategies. Finally, an interface with the open-source high-order mesh generator Gmsh is provided to facilitate its application to practical engineering problems.