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SU‐C‐BRC‐02: Accelerating Linear Boltzmann Transport Equation by An Asymptotic‐Preserving Scheme
Author(s) -
Chen G,
Chen H,
Hong X,
Tang M,
Gao H
Publication year - 2016
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.4955549
Subject(s) - discretization , quadrature (astronomy) , mathematics , boltzmann equation , mathematical analysis , monte carlo method , scattering , grid , finite difference , physics , geometry , quantum mechanics , statistics , optics
Purpose: Linear Boltzmann transport equation (LBTE) is as accurate as the Monte Carlo method for dose calculation. This work is to develop an asymptotic‐preserving (AP) scheme to accelerate the LBTE, i.e., to achieve the same accuracy with significantly reduced number of spatial grids. Methods: In this proof‐of‐concept study, two‐dimensional LBTE is solved by the discrete ordinate method. The Level‐Symmetric (LQn) quadrature set is employed for angular discretization of LBTE. The Henyey‐Greenstein scattering function is used for simulating the anisotropic scattering. For the AP scheme, the anisotropic scattering kernel is discretized as a scattering matrix and its difference with the analytical form is minimized with some constraints that are introduced to preserve the diffusive limit. Since LBTE is linear, the solution on each grid is approximated by linear combination of characteristic solutions and a special solution. A four‐point cell‐centered scheme is used to establish the linear system of the final solution with unknowns and a finite difference scheme connects the unknowns at four edge centers of the cell to solve this system. Results: First, compared with the exact analytical solution, the discrete L2 norm of the numerical error of the proposed method is less than 0.03 percents when the order of quadrature set is larger than 6 (i.e., more than 48 angles), even when the spatial grid is reduced to 8 by 8. Second, when using fewer spatial grids, the proposed method is more accurate than the conventional Source Iteration method. Conclusion: The AP scheme is developed for accelerating LBTE, and the accurate results can be achieved with significantly reduced number of spatial grids. The authors were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000), and the Shanghai Pujiang Talent Program (#14PJ1404500).