A Sparse Grid Discrete Ordinate Discontinuous Galerkin Method for the Radiative Transfer Equation (Communications in Computational Physics, 2021)
The radiative transfer equation is a fundamental equation in transport theory and applications, which is a 5-dimensional PDE in the stationary one-velocity case,leading to great difficulties in numerical simulation. To tackle this bottleneck, we firstuse the discrete ordinate technique to discretize the scattering term, an integral with respect to the angular variables, resulting in a semi-discrete hyperbolic system. Then, wemake the spatial discretization by means of the discontinuous Galerkin (DG) methodcombined with the sparse grid method. The final linear system is solved by the blockGauss-Seidal iteration method. The computational complexity and error analysis aredeveloped in detail, which show the new method is more efficient than the originaldiscrete ordinate DG method. A series of numerical results are performed to validatethe convergence behavior and effectiveness of the proposed method.