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Nonlinear Acceleration of Transport Criticality Problems

H. Park, D. A. Knoll, C. K. Newman

Nuclear Science and Engineering

Volume 172 / Number 1 / September 2012 / Pages 52-65


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We present a nonlinear acceleration algorithm for a transport criticality problem. The algorithm combines the well-known nonlinear diffusion acceleration (NDA) algorithm with a recently developed, Newton-based nonlinear criticality acceleration (NCA) algorithm. The algorithm first employs NDA to reduce the system to scalar flux, then NCA is applied to the resulting drift-diffusion system. We apply a nonlinear elimination technique to eliminate the eigenvalue constraint equation from the Jacobian matrix. Numerical results show that the algorithm can reduce the CPU time by a factor of 30 to 400 compared to traditional power iterations (PIs) combined with standard source iterations and by a factor of 3 to 5 compared to application of NDA combined with inner PIs.

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