Accelerations of the Discrete Ordinate Method for Nadir Viewing Geometries

In this paper we analyze several acceleration techniques for the discrete ordinate method with matrix exponential for the solution of the radiative transfer equation. These techniques include the left eigenvectors matrix approach for computing the inverse of the right eigenvector matrix, the telescoping technique, and the method of false discrete ordinate. The numerical simulations have shown that on average the relative speedup of the left eigenvector matrix approach and the telescoping technique are of about 15% and 30%, respectively