### Abstract

For the safety and the control of a nuclear power plant it is necessary to
simulate the constituent processes on a computer system. The three-dimensional
multigroup neutron diffusion equations are commonly used to describe the
nuclear fission in the reactor core. They form a complicated system of coupled
parabolic partial differential equations (PDEs) whose solution can involve very
intensive computing. In this paper this system of PDEs is discretised using a
special cell-centred mixed finite volume method (NEM-M0) in space, and a method
that combines Crank-Nicholson and the BDF(2)-method in time. The linear
equation systems which arise are solved with Multi-Grid as well as with
preconditioned BiCGStab. The kernel of both solution methods is an effective
Block-SOR method that makes use of the particular structure of the linear
equation systems. The parallelisation strategy is based on a grid partitioning
that distributes the data and the work homogeneously on the processors. Finally
the program was tested for three typical reactor simulation problems on grids
with differing coarseness. The speedup achieved by parallelising Multi-Grid and
preconditioned Bi-CGStab was outstanding for all examples; even superlinear in
some cases. Moreover, the parallel execution times were better than the
parallel execution times of other established reactor simulation codes.