Sparse tensor spherical harmonics approximation in radiative transfer (Q414015)

The process of stationary radiative transfer is presented as a Dirichlet boundary value problem NEWLINE\[NEWLINE Lu=f,\qquad u|_{\partial\Omega_{-}}=0,NEWLINE\]NEWLINE where \(u(x,s)\) is the radiative intensity, \({\partial\Omega_{-}}\) denote inflow part of the boundary of the domain \( \Omega=D\times S^{d_{s}}\) and the operator \(L\) can be split in the form \( L=T+Q_{\sigma}\) with the operator \(T\) that define the transport part and \(Q_{\sigma}\) is the scattering operator. Using the variational formulation of this problem the authors apply two methods to obtain the approximate solution: a Galerkin finite element method in the physical space and a spectral discretization with the harmonics for the angular variable. The graphical behavior of the error is shown for six examples.