Standard and goal-oriented adaptive mesh refinement applied to radiation transport on 2D unstructured triangular meshes

DOI10.1016/j.jcp.2010.10.018zbMath1210.82005OpenAlexW2005867846MaRDI QIDQ617481

Jean C. Ragusa, Ya-qi Wang

Publication date: 21 January 2011

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2010.10.018

zbMATH Keywords

error estimatesadaptive mesh refinementdiscrete ordinates methodradiation transportgoal-oriented mesh refinementdiscontinuous finite element techniques

Mathematics Subject Classification ID

Related Items (20)

Spatial adaptivity of the SAAF and weighted least squares (WLS) forms of the neutron transport equation using constraint based, locally refined, isogeometric analysis (IGA) with dual weighted residual (DWR) error measures ⋮ A high-order/low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations ⋮ Angular Multigrid Preconditioner for Krylov-Based Solution Techniques Applied to theS_nEquations with Highly Forward-Peaked Scattering ⋮ Goal-Based Error Estimation, Functional Correction, h, p and hp Adaptivity of the 1-D Diamond Difference Discrete Ordinate Method ⋮ On the Use of Symmetrized Transport Equation in Goal-Oriented Adaptivity ⋮ Discontinuous finite element solution of the radiation diffusion equation on arbitrary polygonal meshes and locally adapted quadrilateral grids ⋮ Goal-based h-adaptivity of the 1-D diamond difference discrete ordinate method ⋮ Inverse radiative transfer with goal-oriented hp-adaptive mesh refinement: adaptive-mesh inversion ⋮ Minimising the error in eigenvalue calculations involving the Boltzmann transport equation using goal-based adaptivity on unstructured meshes ⋮ Solution of the equation of radiative transfer using a Newton-Krylov approach and adaptive mesh refinement ⋮ Computing enhancement of the nonlinear \(\mathrm{SP}_{\mathrm{N}}\) approximations of radiative heat transfer in participating material ⋮ Fast, low-memory numerical methods for radiative transfer via \(hp\)-adaptive mesh refinement ⋮ Online basis construction for goal-oriented adaptivity in the generalized multiscale finite element method ⋮ Even-parity Boltzmann transport equation applied for response (contributon) flux calculation based on the spatial channel theory ⋮ Entropy-based artificial viscosity stabilization for non-equilibrium grey radiation-hydrodynamics ⋮ Goal-based angular adaptivity applied to a wavelet-based discretisation of the neutral particle transport equation ⋮ An adaptive, hanging-node, discontinuous isogeometric analysis method for the first-order form of the neutron transport equation with discrete ordinate \((S_{\mathrm{N}})\) angular discretisation ⋮ Quadratic serendipity discontinuous finite element discretization for \(S_N\) transport on arbitrary polygonal grids ⋮ Residual Monte Carlo for the One-Dimensional Particle Transport Equation ⋮ Goal-Based Error Estimation for the Multi-Dimensional Diamond Difference and Box Discrete Ordinate (S_N) Methods

Uses Software

• HERA
• FEAPpv

Cites Work

• Adaptive mesh refinement for hyperbolic partial differential equations
• Performance and performance modeling of a parallel algorithm for solving the neutron transport equation
• Local adaptive mesh refinement for shock hydrodynamics
• A posteriori error control in radiative transfer
• An adaptive mesh refinement algorithm for the radiative transport equation
• Goal-oriented \(hp\)-adaptivity for elliptic problems.
• An adaptive higher order method for solving the radiation transport equation on unstructured grids
• Spatial differencing of the transport equation: Positivity vs. accuracy
• Convergence of a Fully Discrete Scheme for Two-Dimensional Neutron Transport
• Partial Differential Equations and the Finite Element Method
• An optimal control approach to a posteriori error estimation in finite element methods
• Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws
• Stabilizedhp-Finite Element Methods for First-Order Hyperbolic Problems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Computing with hp-ADAPTIVE FINITE ELEMENTS
• Spectral/hp Element Methods for Computational Fluid Dynamics
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