AN APPLICATION OF THE FINITE-ELEMENT METHOD TO THE SOLUTION OF THE RADIATIVE-TRANSFER EQUATION

The finite element method is applied to the solution of the RTE for a plane parallel homogeneous slab with absorbing boundaries. This method is shown to be numerically equivalent to the discrete ordinate method, but, differently from that, is exactly flux-conserving in a manner which does not depend on the shape of the phase function. The final form of the solution which is presented does not suffer from any numerical instability. The comparison of the zero-order Fourier component of the intensity obtained with the finite element and the discrete ordinate method demonstrates the better performance of the first for a moderate number of node points in the case of highly asymmetric phase functions, which provides the possibility of obtaining a higher accuracy with a more sparse grid.