Application of the RBF meshless method to the solution of the radiative transport equation

Authors:
Manuel Kindelan;Francisco Bernal;Pedro González-Rodríguez;Miguel Moscoso
Affiliations:
Gregorio Millán Institute, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain;Gregorio Millán Institute, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain;Gregorio Millán Institute, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain;Gregorio Millán Institute, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain
Venue:
Journal of Computational Physics
Year:
2010

Citing 16
Cited 1

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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.