High performance computation of reactor and ADS eigenvalues

Neutron multiplication is the most important property of nuclear reactors and it is usually investigated using various eigenvalue forms of the transport equation. Due to the complex structure of real life reactors these are treated by numerical approximations and the solution methodology is traditionally based on the (inverse) power iteration.

The matrices involved in practical reactor problems are huge and the efficiency of the iteration is very sensitive to the spacing of the eigenvalues. Therefore various enhanced iterative methods and acceleration schemes have been developed for improving the convergence of the algorithm. Due to the practical needs of the nuclear industry these mainly focus on the determination of the fundamental mode of the static eigenvalue equation. The options strech from ancient rebalance methods and shift-based schemes to some recently introduced, elaborate low order accelerators and nonlinear correction schemes.

In contrast to the static eigenvalue problem, the kinetic eigenvalue equations have seen very limited research during the history of computational reactor physics. However, they are expected to play cruical role in innovative nuclear reactor concepts like ADSs (Accelerator Driven Subcritical System), study of neutron fluctuations and instabilities, or the development of on-line reactivity monitoring equipment. Thus it would be important to be able to determine non-fundamental modes of the kinetic equations. Only a minority of the existing computational tools offers some option to determine the kinetic eigenvalues, and almost all of these are based on a simple eigenvalue search wrapped around the k_eff solver and these methods are usually restricted to determining the fundamental mode and they are rather slow.

Very limited research has been done to employ more advanced schemes to the kinetic eigenvalue equations. These prominently focus on the application of various Krylov methods and they are frequently based on diffusion approximation to save computing resources. One particular disadvantage of the recently investigated methodologies lies in the fact that the blind application of such generic algorithms rarely lend themselves for the introduction of more elaborate preconditioning techniques, while experience from the field of fixed source equations shows that efficient solvers insist of using multilayer preconditioning schemes based on the detailed knowledge of the physical background of the problem, in this case neutron transport. These are designed shifting the bulk of the solver's work to the preconditioners and therefore reducing the computational resources spent on expensive transport schemes.

The candidate will investigate the possible exploitation of the physics based preconditioning technology as well as the opportunites offered by alternative iterative algorithms for the solution of these eigenvalue problems and develop efficient codes for solving various forms of the eigenvalue equations. He/she shall devise new numerical schemes for the eigenvalue solver and implement them in his/her own code.