FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method, Part I: Diffusion operator. (July 2015)

• Record Type: Journal Article
• Authors: Frank, Florian; Reuter, Balthasar; Aizinger, Vadym; Knabner, Peter
• Is Part Of: Computers & mathematics with applications. Volume 70:issue 1(2015)
• Page Start: 11
• Page End: 46
• Publication Date: 2015-07
• Subjects: MATLAB -- GNU Octave -- Local discontinuous Galerkin method -- Vectorization -- Open source; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2015.04.013
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This is the first in a series of papers on implementing a discontinuous Galerkin (DG) method as an open source MATLAB/GNU Octave toolbox. The intention of this ongoing project is to provide a rapid prototyping package for application development using DG methods. The implementation relies on fully vectorized matrix/vector operations and is carefully documented; in addition, a direct mapping between discretization terms and code routines is maintained throughout. The present work focuses on a two-dimensional time-dependent diffusion equation with space/time-varying coefficients. The spatial discretization is based on the local discontinuous Galerkin formulation. Approximations of orders zero through four based on orthogonal polynomials have been implemented; more spaces of arbitrary type and order can be easily accommodated by the code structure.