The Davidson method as an alternative to power iterations for criticality calculations

The Davidson method is implemented within the neutron transport core solver parafish to solve k-eigenvalue criticality transport problems. The parafish solver is based on domain decomposition. It uses spherical harmonics (PN method) for angular discretization, and non-conforming finite elements for spatial discretization. The Davidson method is compared to the traditional power iteration method in this context.

► The Davidson method is applied to PN criticality problems.
► It performs more elaborated iterations than the traditional power method.
► It requires no tuning (in contrast to Chebyshev acceleration).
► The total number of iterations is reduced compared to the power method.
► The computing times are cut by a factor 2–3 in our numerical tests.