Application of the RBF Meshless Method to the Solution of the Radiative Transport Equation Articles uri icon

publication date

  • March 2010

start page

  • 1897

end page

  • 1908

issue

  • 5

volume

  • 229

international standard serial number (ISSN)

  • 0021-9991

electronic international standard serial number (EISSN)

  • 1090-2716

abstract

  • In this paper, we introduce a radial basis function collocation method for computing solutions to the time-dependent radiative transfer equation. For these computations, we use finite differences to
    discretize the time coordinate, a discrete ordinate method to discretize
    the directional variable, and an expansion in radial basis functions to
    approximate the spatial dependence of the solution. The main advantages
    of the RBF method are that it does not require any mesh or grid,
    achieves spectral accuracy in multi-dimensions for arbitrary node
    layouts, and it is extremely simple to implement.