## Parallel Solution of the Multigroup Neutron Diffusion Equations

This project has involved the implementation of parallel solution methods, in
particular parallel Multigrid and Krylov-subspace methods, for the efficient
solution of the three-dimensional transient multigroup neutron diffusion
equations, which are used to model the distribution of the neutrons in a
nuclear reactor core. This project was supported in part by the
Siemens AG,
Munich, and a Leonardo da Vinci scholarship from the European Union.
Mathematically those equations
form a non-symmetric system of 2nd-order parabolic partial differential
equations, which is discretised using a non-standard mixed finite volume
discretisation technique. The calculation of the initial condition for this
system involves the solution of a generalised eigenvalue problem. The task to
construct an efficient parallel iterative solution method for the resulting
large non-symmetric linear equation systems was therefore very challenging.
We were able to report a competitive sequential performance of our methods, and
the parallel efficiency of the methods is optimal for up to 10 processors.
Publications:

*R. Scheichl,*
** Parallel Solution of the Transient Multigroup Neutron Diffusion Equations
with Multi-Grid and Preconditioned Krylov-Subspace Methods (Master's Thesis).
** Schriften der Johannes Kepler Universitaet Linz, Vol. ** C21 **,
Trauner-Verlag, Linz, 1997.

*R. Scheichl,*
** Parallel Solvers for the Two-Group Neutron Diffusion Equations of
Reactor Kinetics.** Proceedings of the 11th International
Conference on Domain Decomposition Methods, Greenwich, July 1998 (edited by
C.H. Lai et al.), 1999. [PostScript file]

*R. Scheichl,*
** Parallel Solvers for the Transient Multigroup Neutron Diffusion Equations.
** International Journal for Numerical Methods in Engineering
** 47**:1751-1771, 2000.
[Abstract]
[PostScript
file]

The code, which implements the developed methods, has been included
(by Dr. M. Paffrath) into the nuclear power plant simulation code RELAP5/PANBOX
of the Siemens AG Operating Division
KWU, which is used for the safety analysis and control of nuclear power
plants. The performance of the methods within this package and further
strategies to enhance the efficiency have also been presented (by Dr. H.
Finnemann) on the **Annual Meeting of the
American Nuclear Society 1999** in
Boston:
*H. Finnemann and R. Scheichl,*
** Efficiency Enhancements of Coupled RELAP5/PANBOX Calculations Using
Adaptive Methods.** Transactions of the American Nuclear Society for the
Annual Meeting, Boston, June 1999. [WordDocument]

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