Professor Lewis' research includes combining finite element with other methods for the solution of the Boltzmann equation for radiation transport problems in six-dimensional space-angle-energy phase space. Applications range from radiative heat transfer to the simulation of neutron transport in nuclear reactor cores. His current investigations are focused on neutron transport methods for treating the complex interactions between fuel-coolant lattices structures and more global effects in large power reactor cores. Under investigation are hybrid finite element and finite subelement formulations for treating spatial variables, tailored spherical harmonic expansions in angle, space-angle-energy adaptive grid algorithms, and response matrix solution methods for parallel computers.