Discontinuous finite element solution of the radiation diffusion equation on arbitrary polygonal meshes and locally adapted quadrilateral grids
Abstract
In this paper, we propose a piecewise linear discontinuous (PWLD) finite element discretization of the diffusion equation for arbitrary polygonal meshes. It is based on the standard diffusion form and uses the symmetric interior penalty technique, which yields a symmetric positive definite linear system matrix. A preconditioned conjugate gradient algorithm is employed to solve the linear system. Piecewise linear approximations also allow a straightforward implementation of local mesh adaptation by allowing unrefined cells to be interpreted as polygons with an increased number of vertices. Several test cases, taken from the literature on the discretization of the radiation diffusion equation, are presented: random, sinusoidal, Shestakov, and Z meshes are used. The last numerical example demonstrates the application of the PWLD discretization to adaptive mesh refinement.
 Authors:
 Publication Date:
 OSTI Identifier:
 22382158
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 280; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; APPROXIMATIONS; DIFFUSION; DIFFUSION EQUATIONS; FINITE ELEMENT METHOD; IMPLEMENTATION; MATRICES; RANDOMNESS; SYMMETRY
Citation Formats
Ragusa, Jean C., Email: jean.ragusa@tamu.edu. Discontinuous finite element solution of the radiation diffusion equation on arbitrary polygonal meshes and locally adapted quadrilateral grids. United States: N. p., 2015.
Web. doi:10.1016/J.JCP.2014.09.013.
Ragusa, Jean C., Email: jean.ragusa@tamu.edu. Discontinuous finite element solution of the radiation diffusion equation on arbitrary polygonal meshes and locally adapted quadrilateral grids. United States. doi:10.1016/J.JCP.2014.09.013.
Ragusa, Jean C., Email: jean.ragusa@tamu.edu. 2015.
"Discontinuous finite element solution of the radiation diffusion equation on arbitrary polygonal meshes and locally adapted quadrilateral grids". United States.
doi:10.1016/J.JCP.2014.09.013.
@article{osti_22382158,
title = {Discontinuous finite element solution of the radiation diffusion equation on arbitrary polygonal meshes and locally adapted quadrilateral grids},
author = {Ragusa, Jean C., Email: jean.ragusa@tamu.edu},
abstractNote = {In this paper, we propose a piecewise linear discontinuous (PWLD) finite element discretization of the diffusion equation for arbitrary polygonal meshes. It is based on the standard diffusion form and uses the symmetric interior penalty technique, which yields a symmetric positive definite linear system matrix. A preconditioned conjugate gradient algorithm is employed to solve the linear system. Piecewise linear approximations also allow a straightforward implementation of local mesh adaptation by allowing unrefined cells to be interpreted as polygons with an increased number of vertices. Several test cases, taken from the literature on the discretization of the radiation diffusion equation, are presented: random, sinusoidal, Shestakov, and Z meshes are used. The last numerical example demonstrates the application of the PWLD discretization to adaptive mesh refinement.},
doi = {10.1016/J.JCP.2014.09.013},
journal = {Journal of Computational Physics},
number = ,
volume = 280,
place = {United States},
year = 2015,
month = 1
}

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