Analysis of a numerical solver for radiative transport equation

DOI10.1090/S0025-5718-2012-02605-6zbMath1268.65165OpenAlexW1973433413WikidataQ38969952 ScholiaQ38969952MaRDI QIDQ4911897

Hao Gao, Hong-Kai Zhao

Publication date: 20 March 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2012-02605-6

zbMATH Keywords

convergenceerror estimatesfinite element methodfinite difference methoddiscontinuous Galerkin methodradiative transport equationdiscrete ordinate methodsource iterationHenyey-Greenstein function

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Radiative transfer in astronomy and astrophysics (85A25)

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An optimal cascadic multigrid method for the radiative transfer equation ⋮ Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method ⋮ On iterative algorithms for quantitative photoacoustic tomography in the radiative transport regime ⋮ Radiative transfer with delta-Eddington-type phase functions ⋮ On a family of discontinuous Galerkin fully-discrete schemes for the wave equation ⋮ A hybrid reconstruction approach for absorption coefficient by fluorescence photoacoustic tomography ⋮ A weak Galerkin finite element method for a type of fourth order problem arising from fluorescence tomography ⋮ A spherical harmonic discontinuous Galerkin method for radiative transfer equations with vacuum boundary conditions ⋮ Image reconstruction for diffuse optical tomography based on radiative transfer equation ⋮ Quantitative PAT with simplified P _N approximation

Cites Work

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• Discrete-Ordinate Discontinuous Galerkin Methods for Solving the Radiative Transfer Equation
• Finite Element Collocation Methods for First Order Systems
• Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes
• A Fast-Forward Solver of Radiative Transfer Equation
• An Optimal-Order Error Estimate for the Discontinuous Galerkin Method
• An Analysis of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation

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