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 …

We propose a multilevel approach for trace systems resulting from hybridized discontinuous
Galerkin (HDG) methods. The key is to blend ideas from nested dissection, domain …

Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and
local polynomial degree adaptivity are revisited. Hybridization techniques are employed to …

We introduce a new preconditioner for a recently developed pressure-robust hybridized
discontinuous Galerkin (HDG) finite element discretization of the Stokes equations. A feature …

The mass flow rate of Poiseuille flow of rarefied gas through long ducts of two-dimensional
cross-sections with arbitrary shape is critical in the pore-network modeling of gas transport in …

We propose a uniform block-diagonal preconditioner for condensed (div)-conforming
hybridizable discontinuous Galerkin schemes for parameter-dependent saddle point …

In the present article, we describe the implementation of the finite element numerical
integration algorithm for the Intel Iris Xe-LP Graphics Processing Unit. This GPU is a direct …

We present a scalable block preconditioning strategy for the trace system arising from the
high-order hybridized discontinuous Galerkin (HDG) discretization of incompressible …

In the present article, we describe the implementation of the finite element numerical
integration algorithm for the Xeon Phi coprocessor. The coprocessor was an extension of the …

This study presents a new framework to solve the coupled semilinear elliptic equation by the
domain decomposition algorithm. Unlike the traditional domain decomposition algorithm, the …