A Nested FGMRES Method for Parallel Calculation of Nuclear Reactor Transients1

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A semi-iterative method based on a nested application of Flexible Generalized Minimum Residual)FGMRES) was developed to solve the linear systems resulting from the application of the discretized two-phase hydrodynamics equations to nuclear reactor transient problems. The complex three-dimensional reactor problem is decomposed into simpler, more manageable problems which are then recombined sequentially by GMRES algorithms. Mathematically, the method consists of using an “inner” level GMRES to solve the preconditioner equation for an “outer” level GMRES. Applications were performed on practical, three-dimensional models of operating Pressurized Water Reactors (PWR). Serial and parallel applications were performed for a reactor model with two different details in the core representation. When appropriately tight convergence was enforced at each GMRES level, the results of the semi-iterative solver were in agreement with existing direct solution methods. For the larger model tested, the serial performance of GMRES was about a factor of 3 better than the direct solver and the parallel speedups were about 4 using 13 processors of the INTEL Paragon. Thus, for the larger problem over an order of magnitude reduction in the execution time was achieved indicating that the use of semi-iterative solvers and parallel computing can considerably reduce the computational load for practical PWR transient calculations.

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