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Title: Scalable Nonlinear Solvers for Fully Implicit Coupled Nuclear Fuel Modeling. Final Report

The focus of the project is on the development and customization of some highly scalable domain decomposition based preconditioning techniques for the numerical solution of nonlinear, coupled systems of partial differential equations (PDEs) arising from nuclear fuel simulations. These high-order PDEs represent multiple interacting physical fields (for example, heat conduction, oxygen transport, solid deformation), each is modeled by a certain type of Cahn-Hilliard and/or Allen-Cahn equations. Most existing approaches involve a careful splitting of the fields and the use of field-by-field iterations to obtain a solution of the coupled problem. Such approaches have many advantages such as ease of implementation since only single field solvers are needed, but also exhibit disadvantages. For example, certain nonlinear interactions between the fields may not be fully captured, and for unsteady problems, stable time integration schemes are difficult to design. In addition, when implemented on large scale parallel computers, the sequential nature of the field-by-field iterations substantially reduces the parallel efficiency. To overcome the disadvantages, fully coupled approaches have been investigated in order to obtain full physics simulations.
Authors:
 [1] ;  [2] ;  [1] ;  [2] ;  [3]
  1. Univ. of Colorado, Boulder, CO (United States). Dept. of Computer Science
  2. Columbia Univ., New York, NY (United States)
  3. Idaho National Lab. (INL), Idaho Falls, ID (United States)
Publication Date:
OSTI Identifier:
1158778
Report Number(s):
DOE--06ER25784
TRN: US1500350
DOE Contract Number:
FC02-06ER25784
Resource Type:
Technical Report
Research Org:
Univ. of Colorado, Boulder, CO (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS; PARTIAL DIFFERENTIAL EQUATIONS; NUCLEAR FUELS; NONLINEAR PROBLEMS; NUMERICAL SOLUTION; COMPUTERIZED SIMULATION; THERMAL CONDUCTION; OXYGEN; DEFORMATION; SOLIDS; TRANSPORT; PROGRESS REPORT