Finite element approximation to the even-parity transport equation

The finite element method is a procedure for reducing partial differential equations to sets of simultaneous algebraic equations suitable for solution on a digital computer. In addressing neutron transport systems, two approahces have been taken, one using discrete ordinates approximations to the conventional form of the transport equation. The second, developed here uses a variational principle as a point of departure for the application of finite elements to neutron transport problems. To formulate finite element methods variational y, the within-group transport equation first is cast into the second-order form that is even parity in angle. The resulting equation is self-adjoint, and may be expressed as a variational principle; the even-parity transport equation is the Euler-Lagrange equation that results from minimizing a corresponding functional. Finite element approximations are than forms of the Ritz procedure provided that the trial functions are continuous in space. Because the dependent variable is the even-parity flux components, and one-half the conventional number of unknowns is required for a given level of angular approximations. Applications to a variety of transport problem classes is analyzed in succeeding sections inlcuding fine mesh multigroup computational procedures and coarse mesh methods