Reference documentation of hpGEM

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INTRODUCTION

hpGEM is a C++ software framework for discontinuous Galerkin method. This framework is intended to those who want to easily develop and apply discontinuous Galerkin methods for various physical problems, especially partial differential equations, arising from fluid mechancis and electro-magnetism. Using HPGEM, one can numerically solve the simplest class room examples such as linear advection and Burgers equations to the most complicated practical examples such as shallow water, Euler, Navier-Stokes and Maxwell equations.

The library was developed using object-oriented programming technique and written using C++ templates to support reusable software and generic programming aspects. In this documentation, classes and functions provided by the library are described in details.

An alpha version of the hpGEM package hpgem.v1.0.0 is now available for download. It employs the following external packages:

• Boost C++ libraries.
• Boost numeric bindings.
• Intel Math Kernel Library.
• Lapack, linear algebraic package.
• UMFPACK, a set of routines for solving unsymmetric sparse linear systems.
• PETSc, Portable, Extensible Toolkit for Scientific Computation

Hence it is a prerequisite to download and install the above packages for a complete installation of hpGEM. See download and installation instructions.

Installation instructions

Applications developed with hpGEM

Information For Developers

Meet the team

Publications

W.E.H. Sollie, J.J.W. van der Vegt and O. Bokhove, Space-time discontinous Galerkin Finite Element Method for two-fluid flows. J. Comp. Phys., Vol. 230, pp. 789-817, 2011

S. Rhebergen, O. Bokhove and J.J.W. van der Vegt, Discontinuous Galerkin finite element method for shallow two-phase flows, Comp. Meth. Appl. Mech. Eng., Vol. 195, Issues 5-8, pp. 819-830, 2009, doi:10.1016/j.cma.2008.10.019.

L. Pesch and J.J.W. van der Vegt, A discontinuous Galerkin finite element discretization of the Euler equations for compressible and incompressible fluids, J. Comp. Phys., Vol. 227, No. 11, pp. 5426-5446, 2008, doi:10.1016/j.jcp.2008.01.046.

D. Sarmany, M.A. Botchev and J.J.W. van der Vegt, Dispersion and Dissipation Error in High-Order Runge-Kutta Discontinuous Galerkin Discretisations of the Maxwell Equations, J. Sci. Comp., Vol. 33, no. 1, pp. 47-74, 2007, doi:10.1007/s10915-007-9143-y.

L. Pesch, A. Bell, W.E.H. Sollie, V.R. Ambati, O. Bokhove, J.J.W. van der Vegt, hpGEM – A software framework for discontinuous Galerkin finite-element methods, ACM Trans. Math. Soft., Vol. 33, Number 4, 2007, doi.acm.org/10.1145/1268776.1268778.