RTE_MG: Multigrid Solver of RTE

Description
  

 

RTE_MG refers to multigrid solver of radiative transfer equation (RTE). RTE_MG aims at solving steady-state or frequency-domain RTE with the medium of

a) complex geometry, e.g., for small animals, human organs and so on;

b) hetergeneous or discontinuous absorption and scattering coefficients;

c) different regimes, such as transport regime or diffusive regime;

d) general phase function (scattering kernel), with the default as Henyey-Greenstein phase function;

e) vacuum boundary condition or reflection boundary condition.

In
RTE_MG, we use a direct angular discretization by finite element method, and upwind type of spatial discretization by discontinuous Galerkin finite element method that preserves properties of both scattering and differential operators of RTE. To solve the large linear system after discretization, we construct an efficient iterative scheme based on Gauss-Seidel and proper angular dependent ordering. With this iterative scheme as the relaxation, various multigrid methods are implemented in both angular and physical space. Our algorithm can deal with different scattering regimes efficiently. Although we emphasize applications in optical molecular imaging, our method may be applied to neutron transport, atmospheric radiative transfer, heat transfer or others.

 

Performance (RTE v.s. MC): here.

     
      

    References

    1. H. Gao* and H. Zhao. A fast forward solver of radiative transfer equation. Transport Theory and Statistical Physics. 38 149-192, 2009. [VIEW]
    2. H. Gao*, L. Phan and Y. Lin. Parallel multigrid solver of radiative transfer equation for photon transport via graphics processing unit. Journal of Biomedical Optics. 17 096004, 2012. [VIEW]
    3. H. Gao* and H. Zhao. Analysis of a numerical solver for radiative transport equation. Mathematics of Computation, 82 153-172, 2013. [VIEW]
    4. H. Gao* and H. Zhao. A multilevel and multigrid optical tomography based on radiative transfer equation. Proceedings of SPIE (Munich, Germany, 2009). [VIEW]
    5. H. Gao* and H. Zhao. Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 regularization. Optics Express. 18 1854-1871, 2010. [VIEW]
    6. H. Gao* and H. Zhao. Multilevel bioluminescence tomography based on radiative transfer equation Part 2: total variation and l1 data fidelity. Optics Express. 18 2894-2912, 2010. [VIEW]


    Codes (C version)

    • RTE_1D:     1D multigrid solver of steady-state RTE.
    • RTE_1D_w: 1D multigrid solver of frequency-domain RTE.
    • RTE_2D:     2D multigrid solver of steady-state RTE.
    • RTE_2D_w: 2D multigrid solver of frequency-domain RTE.
    • RTE_3D:     3D multigrid solver of steady-state RTE.
    • RTE_3D_w: 3D multigrid solver of frequency-domain RTE.
    • IMPORTANT: you need COMSOL/MATLAB interface in order to generate 3D mesh in the sample mesh generation file. When you use other mesh softwares, please match the data structure as required by the input for solvers.

    Codes (MATLAB version)

    • RTE_2D_MATLAB: 2D multigrid solver of frequency-domain/steady-state RTE.

    GPU Codes (MATLAB mex version)

    • The GPU solver is available here.

    Note: In case these codes "do not work" for your purposes, you may contact us for further discussions or code modifications.

    Contact: hao.gao.2012 AT gmail.com


    Subpages (1): RTE v.s. MC