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DEVELOPMENT OF A MULTIPLE PERTURBATION MONTE CARLO METHOD FOR EIGENVALUE PROBLEMS AND IMPLEMENTATION ON PARALLEL PROCESSORSAmitava Majumdar Chairperson: William R. Martin

We have developed a Monte Carlo method that calculates multiple perturbation effects in the eigenvalue (K) of the Boltzmann transport equation for neutrons from a single Monte Carlo simulation. Two Monte Carlo techniques, source iteration and fission matrix approaches, have been described. We have shown that subtracting two independent Monte Carlo simulations for eigenvalue perturbation calculation encounters difficulties. It is necessary to utilize some type of Monte Carlo perturbation technique. We have shown that the combination of the correlated sampling and source iteration methods encounters difficulties in calculating eigenvalue perturbations. When the correlated sampling approach is combined with the fission matrix approach, it can successfully evaluate eigenvalue perturbations. We have implemented the idea of performing Monte Carlo simulation in an artificial reference system. Utilizing the fission matrix approach, correlated sampling, and an artificial reference system, we have developed the multiple perturbation technique. The actual simulation is done in an artificial reference system and all the perturbed and unperturbed systems' fission matrices are correlated to that reference system. At the end of the simulation, the dominant eigenvalue of the unperturbed and all perturbed fission matrices are evaluated numerically. This provides us with multiple $\Delta$Ks from a single Monte Carlo simulation. We have tested this method for different test problems and the results compared well with that of the TWODANT S_N transport code. This method allowed significant savings in computational effort.

We have implemented fixed source and eigenvalue algorithms for neutron transport on three different parallel machines, the BBN Butterfly, KSR-1, and IBM-SP2. We have addressed the issue of parallel random number generators and showed how the fixed source and eigenvalue parallel algorithms differ. Theoretical models for speedups have been developed and have compared well with the observed speedups. Close to linear speedups were observed for many of the test problems.