PROJECTION-BASED PARAMETRIC MODEL ORDER REDUCTION FOR TRANSPORT SIMULATION BASED ON AFFINE DECOMPOSITION OF THE OPERATORS

Model-order reduction (MOR) is a technique utilized to reduce the computational complexity of numerical simulations of physical phenomena. When the solution space of the underlying mathematical model is known to a high degree of confidence, the low cost of parametric MOR is especially attractive. The phenomenon of interest is the neutral particle radiation transport equation. The full-order particle conservation equation for transport is a linear partial differential equation, typically discretized using discontinuous finite element methods and solved with a highly efficient matrix-free method known as transport sweeping. Efficiently applying parametric MOR to a matrix-free linear full-order solver is nontrivial in that one must choose between the luxury of minimal intrusion or the long-term efficiency of the reduced-order model (ROM). The authors present and compare two methods of constructing a parametric ROM using proper orthogonal decomposition (POD) with the method of snapshots. The first approach, based upon previous work, is minimally invasive, exploiting transport sweeps to build a ROM. The second, more intrusive, approach applies the affine decomposition of the transport operator. Both methods are evaluated by their performance over several test cases.