Spatial and angular variation and discretization of the self-adjoint transport operator

摘要

This mathematical treatise begins with a variational derivation of a second-order, self-adjoint form of the transport equation. Next, a space variational functional whose minimization solves the transport equation is derived. A one-dimensional example is given. Then, (ital S(sub N)) and (ital P(sub N)) discretized functionals are expressed. Next, the surface contributions to the functionals are discretized. Finally, the explicit forms of the (rvec D) and (rvec H) matrices are given for four different geometries: hexahedron, wedge, tetrahedron, and pyramid.