Extension of modified power method to two-dimensional problems

In this study, the generalized modified power method was extended to two-dimensional problems. A direct application of the method to two-dimensional problems was shown to be unstable when the number of requested eigenmodes is larger than a certain problem dependent number. The root cause of this instability has been identified as the degeneracy of the transfer matrix. In order to resolve this instability, the number of sub-regions for the transfer matrix was increased to be larger than the number of requested eigenmodes; and a new transfer matrix was introduced accordingly which can be calculated by the least square method. The stability of the new method has been successfully demonstrated with a neutron diffusion eigenvalue problem and the 2D C5G7 benchmark problem.

[1]  Thomas E. Booth,et al.  Computing the Higher k-Eigenfunctions by Monte Carlo Power Iteration: A Conjecture , 2003 .

[2]  T. Booth.  Power Iteration Method for the Several Largest Eigenvalues and Eigenfunctions , 2006 .

[3]  Toshihiro Yamamoto.  Convergence of the second eigenfunction in Monte Carlo power iteration , 2009 .

[4]  E. Lewis,et al.  Benchmark specification for Deterministic 2-D/3-D MOX fuel assembly transport calculations without spatial homogenisation (C5G7 MOX) , 2001 .

[5]  Dong Wook Lee,et al.  COARSE MESH FINITE DIFFERENCE ACCELERATION OF DISCRETE ORDINATE NEUTRON TRANSPORT CALCULATION EMPLOYING DISCONTINUOUS FINITE ELEMENT METHOD , 2014 .

[6]  T. Booth,et al.  Multiple Extremal Eigenpairs of Very Large Matrices by Monte Carlo Simulation , 2008, 0807.1273.

[7]  Bojan Petrovic,et al.  Implementation of the modified power iteration method to two-group Monte Carlo eigenvalue problems , 2011 .

[8]  Toshihiro Yamamoto.  Non-regionwise weight cancellation for Monte Carlo higher order criticality calculations using kernel density estimator , 2011 .

[9]  T E Booth,et al.  Monte Carlo determination of multiple extremal eigenpairs. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Bojan Petrovic,et al.  Calculating the Second Eigenpair in Criticality Calculations Using the Monte Carlo Method with Source Points Pairing as an Efficient Net-Weight (Cancellation) Algorithm , 2012 .

[11]  E. Larsen,et al.  Hybrid Monte Carlo-CMFD Methods for Accelerating Fission Source Convergence , 2013 .

[12]  Peng Zhang,et al.  A general solution strategy of modified power method for higher mode solutions , 2016, J. Comput. Phys..

[13]  Thomas E. Booth,et al.  Exact Regional Monte Carlo Weight Cancellation for Second Eigenfunction Calculations , 2010 .

[14]  Thomas E. Booth,et al.  Multiple extremal eigenpairs by the power method , 2008, J. Comput. Phys..

[15]  Thomas E. Booth,et al.  Improved criticality convergence via a modified Monte Carlo iteration method , 2009 .