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Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

Mohan, PS; Tarvainen, T; Schweiger, M; Pulkkinen, A; Arridge, SR; (2011) Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements. J COMPUT PHYS , 230 (19) 7364 - 7383. 10.1016/j.jcp.2011.06.004.

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Abstract

We propose the P-N approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P-N approximation is compared against Monte Carlo simulations and other state-of-the-art methods. (C) 2011 Elsevier Inc. All rights reserved.

Type:Article
Title:Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements
DOI:10.1016/j.jcp.2011.06.004
Keywords:Radiative transport equation, P-N approximation, Finite element method, Variable order P-N, OPTICAL TOMOGRAPHY, PHOTON MIGRATION, FREQUENCY-DOMAIN, DIFFUSION CALCULATIONS, MODEL, RECONSTRUCTION, REGIONS, SCATTERING
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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