Multi-hp adaptive discontinuous Galerkin methods for simplified P approximations of 3D radiative transfer in non-gray media

Abstract

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A Refinement-by-Superposition Approach to Fully Anisotropic hp-Refinement for Improved Efficiency in CEM

“…In such cases, isotropic h-refinement may introduce more DoFs than necessary to improve solution accuracy. Anisotropic h-adaptivity can therefore contribute to improved efficiency or even faster convergence rates by introducing new unknowns in a more frugal manner [4]. Likewise, anisotropic p-adaptivity permits increasing a cell's polynomial expansion order in only one direction to drive more efficient improvements to the solution accuracy.…”

“…That is not to say that the necessary theoretical foundations are absent [1], [2], rather, the requisite implementation complexity has impeded adoption of these techniques. The implementation difficulties can be avoided entirely by employing triangular or tetrahedral discretizations [3] or a discontinuous Galerkin Formulation [4]; however, nonrectangular cells are sub optimal for the linear independence of unit vectors in many CEM applications, and discontinuous Galerkin formulations do not maximize per-DoF efficiency. Therefore, we explore a far less burdensome approach to Jeremiah Corrado, Jake J. Harmon, and Branislav M. Notaroš are with the department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523-1373 USA (e-mail: jcorrado@rams.colostate.edu, jake.harmon@ieee.org, branislav.notaros@colostate.edu).…”

An Adaptive Moving Mesh Discontinuous Galerkin Method for the Radiative Transfer Equation

“…In [21], an adaptive mesh refinement (AMR) algorithm has been formulated and imple-mented for the RTE by minimizing the spatial discretization error. In [12], hp-adaptive DG methods have been developed for the numerical solution of simplified P N approximations of radiative transfer in non-grey semitransparent media and it has been found that it is possible to approximate the radiative field with a significantly lower computational cost than solving the equations using the conventional finite element method. In [11], hp-adaptive methods have been develop based on a short-characteristics approach embedded in the discontinuous finite element framework.…”