Acceleration of k-Eigenvalue / Criticality Calculations using the Jacobian-Free Newton-Krylov Method

Journal Article · Mon Jan 31 23:00:00 EST 2011 · Nuclear Science and Engineering

DOI:https://doi.org/10.13182/NSE09-89· OSTI ID:1010691

Knoll, Dana; Park, HyeongKae; Newman, Chris

We present a new approach for the $$k$$--eigenvalue problem using a combination of classical power iteration and the Jacobian--free Newton--Krylov method (JFNK). The method poses the $$k$$--eigenvalue problem as a fully coupled nonlinear system, which is solved by JFNK with an effective block preconditioning consisting of the power iteration and algebraic multigrid. We demonstrate effectiveness and algorithmic scalability of the method on a 1-D, one group problem and two 2-D two group problems and provide comparison to other efforts using silmilar algorithmic approaches.

• Research Organization: Idaho National Laboratory (INL)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC07-05ID14517
• OSTI ID: 1010691
• Report Number(s): INL/JOU-09-17332
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 2 Vol. 167; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ACCELERATION
CRITICALITY
NONLINEAR PROBLEMS
Newton-Krylov Methods
eigenvalue problems