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A Theoretical Analysis of Anderson Acceleration and Its Application in Multiphysics Simulation for Light-Water Reactors.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	A Theoretical Analysis of Anderson Acceleration and Its Application in Multiphysics Simulation for Light-Water Reactors./
Author:	Toth, Alexander Raymond.
Description:	1 online resource (216 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
Contained By:	Dissertation Abstracts International78-08B(E).
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369622584

A Theoretical Analysis of Anderson Acceleration and Its Application in Multiphysics Simulation for Light-Water Reactors.
Toth, Alexander Raymond.

A Theoretical Analysis of Anderson Acceleration and Its Application in Multiphysics Simulation for Light-Water Reactors. - 1 online resource (216 pages)

Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

In this work, we are concerned with both contributing to the theoretical foundation for Anderson acceleration, a method for accelerating the convergence rate of Picard iteration, and evaluating its performance in the context of coupled multiphysics problems in nuclear reactor simulation. Anderson acceleration proceeds by maintaining a depth of previous iterate information in order to compute a new iterate as a linear combination of previous evaluations of the fixed-point map, where the linear combination coefficients are obtained by solving a linear leastsquares problem. Prior to this work, theory for this method was fairly sparse, dealing mainly with showing its relation to quasi-Newton multisecant updating and, when applied to linear problems, GMRES iteration. The analysis presented in this work significantly expands upon the theory for this method. As this method is intended as an acceleration method for Picard iteration, our analysis concerns problems for which Picard iteration is convergent, namely when the fixed-point mapping is contractive. We present analysis which represent the first convergence results for limited-memory variations of Anderson acceleration and for nonlinear problems. Additionally, we present analysis for several variations on the standard Anderson acceleration method. In particular, we consider a variation which adjusts the memory utilization in order to maintain good conditioning of the least-squares problem, and we present local improvement results for the case in which the fixed-point map can only be evaluated approximately.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369622584Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

A Theoretical Analysis of Anderson Acceleration and Its Application in Multiphysics Simulation for Light-Water Reactors.
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100 1 $a Toth, Alexander Raymond. $3 1180818
245 1 2 $a A Theoretical Analysis of Anderson Acceleration and Its Application in Multiphysics Simulation for Light-Water Reactors.
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300 $a 1 online resource (216 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
500 $a Adviser: Carl Kelley.
502 $a Thesis (Ph.D.) $c North Carolina State University $d 2016.
504 $a Includes bibliographical references
520 $a In this work, we are concerned with both contributing to the theoretical foundation for Anderson acceleration, a method for accelerating the convergence rate of Picard iteration, and evaluating its performance in the context of coupled multiphysics problems in nuclear reactor simulation. Anderson acceleration proceeds by maintaining a depth of previous iterate information in order to compute a new iterate as a linear combination of previous evaluations of the fixed-point map, where the linear combination coefficients are obtained by solving a linear leastsquares problem. Prior to this work, theory for this method was fairly sparse, dealing mainly with showing its relation to quasi-Newton multisecant updating and, when applied to linear problems, GMRES iteration. The analysis presented in this work significantly expands upon the theory for this method. As this method is intended as an acceleration method for Picard iteration, our analysis concerns problems for which Picard iteration is convergent, namely when the fixed-point mapping is contractive. We present analysis which represent the first convergence results for limited-memory variations of Anderson acceleration and for nonlinear problems. Additionally, we present analysis for several variations on the standard Anderson acceleration method. In particular, we consider a variation which adjusts the memory utilization in order to maintain good conditioning of the least-squares problem, and we present local improvement results for the case in which the fixed-point map can only be evaluated approximately.
520 $a With respect to coupled multiphysics problems, we examine Anderson acceleration as an alternative to Picard iteration in the context of black-box code coupling in nuclear reactor simulation. Picard iteration comes with several drawbacks in this context, namely relatively slow convergence and poor robustness. To test the potential for Anderson acceleration to improve upon the weaknesses of Picard iteration, we first consider a one-dimensional model problem which recreates several phenomena observed in higher fidelity couplings. We then consider the Tiamat code coupling being developed as part of the Consortium for Advanced Simulation of LWRs (CASL). Tiamat couples the Bison fuel performance code with the MPACT neutronics and COBRA-TF thermal hydraulics codes to provide a tool for pellet-cladding interaction analysis. Prior to this work, this code utilized exclusively Picard iteration to couple these single-physics codes. We overview Tiamat and describe how Anderson acceleration has been integrated into this coupling by posing the coupled system as a fixed-point problem in terms of coupling parameters. We then examine the performance gains obtained from utilizing Anderson acceleration for this coupling by considering parameter studies at various problem sizes.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
650 4 $a Nuclear engineering. $3 655622
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
690 $a 0552
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a North Carolina State University. $3 845424
773 0 $t Dissertation Abstracts International $g 78-08B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10583579 $z click for full text (PQDT)