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A Theoretical Analysis of Anderson A...

Toth, Alexander Raymond.

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

Record Type:	Electronic resources : Monograph/item
Title/Author:	A Theoretical Analysis of Anderson Acceleration and Its Application in Multiphysics Simulation for Light-Water Reactors./
Author:	Toth, Alexander Raymond.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
Description:	216 p.
Notes:	Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
Contained By:	Dissertation Abstracts International78-08B(E).
Subject:	Applied mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10583579
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. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 216 p.

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

Thesis (Ph.D.)--North Carolina State University, 2016.

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.

ISBN: 9781369622584Subjects--Topical Terms:

2122814
Applied mathematics.

A Theoretical Analysis of Anderson Acceleration and Its Application in Multiphysics Simulation for Light-Water Reactors.
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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 216 p.
500 $a Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
500 $a Adviser: Carl Kelley.
502 $a Thesis (Ph.D.)--North Carolina State University, 2016.
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.
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