Most high-fidelity computer simulations rely on very fine meshes. The size of a 3D problem increases by a factor of 8 when the mesh is made twice as fine, and it can quickly get out of hand. Proper Generalized Decomposition (PGD) is one method for that allows computers to solve very large multidimensional problems. This project uses the PGD method to solve neutron transport problems and multiphysics nuclear reactor analysis problems.

PGD transforms a multidimensional PDE into a set of coupled single-dimensional PDEs. The solutions to the set of equations are added as basis functions to a Reduced Order Model (ROM). New basis functions are progressively added until the ROM attains sufficient precision. We are implementing a PGD solver for neutron transport and coupling it with thermal-fluid simulations to produce a fast, scalable multiphysics nuclear reactor analysis code.