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Domain decomposition methods for advection dominated linear-quadratic elliptic optimal control problems

Computer Methods in Applied Mechanics and Engineering

Bartlett, Roscoe B.; Heinkenschloss, Matthias; Ridzal, Denis; van Bloemen Waanders, Bart G.

We present an optimization-level domain decomposition (DD) preconditioner for the solution of advection dominated elliptic linear-quadratic optimal control problems, which arise in many science and engineering applications. The DD preconditioner is based on a decomposition of the optimality conditions for the elliptic linear-quadratic optimal control problem into smaller subdomain optimality conditions with Dirichlet boundary conditions for the states and the adjoints on the subdomain interfaces. These subdomain optimality conditions are coupled through Robin transmission conditions for the states and the adjoints. The parameters in the Robin transmission condition depend on the advection. This decomposition leads to a Schur complement system in which the unknowns are the state and adjoint variables on the subdomain interfaces. The Schur complement operator is the sum of subdomain Schur complement operators, the application of which is shown to correspond to the solution of subdomain optimal control problems, which are essentially smaller copies of the original optimal control problem. We show that, under suitable conditions, the application of the inverse of the subdomain Schur complement operators requires the solution of a subdomain elliptic linear-quadratic optimal control problem with Robin boundary conditions for the state. Numerical tests for problems with distributed and with boundary control show that the dependence of the preconditioners on mesh size and subdomain size is comparable to its counterpart applied to a single advection dominated equation. These tests also show that the preconditioners are insensitive to the size of the control regularization parameter.

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TYPE Journal Article YEAR 2006
ScopusOSTI

Ideas underlying quantification of margins and uncertainties(QMU): a white paper

Pilch, Martin P.; Trucano, Timothy G.

This report describes key ideas underlying the application of Quantification of Margins and Uncertainties (QMU) to nuclear weapons stockpile lifecycle decisions at Sandia National Laboratories. While QMU is a broad process and methodology for generating critical technical information to be used in stockpile management, this paper emphasizes one component, which is information produced by computational modeling and simulation. In particular, we discuss the key principles of developing QMU information in the form of Best Estimate Plus Uncertainty, the need to separate aleatory and epistemic uncertainty in QMU, and the risk-informed decision making that is best suited for decisive application of QMU. The paper is written at a high level, but provides a systematic bibliography of useful papers for the interested reader to deepen their understanding of these ideas.

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TYPE SAND Report YEAR 2006
OSTIDOI

ChISELS 1.0: theory and user manual :a theoretical modeler of deposition and etch processes in microsystems fabrication

Musson, Lawrence M.; Schmidt, Rodney C.; Ho, Pauline H.; Plimpton, Steven J.

Chemically Induced Surface Evolution with Level-Sets--ChISELS--is a parallel code for modeling 2D and 3D material depositions and etches at feature scales on patterned wafers at low pressures. Designed for efficient use on a variety of computer architectures ranging from single-processor workstations to advanced massively parallel computers running MPI, ChISELS is a platform on which to build and improve upon previous feature-scale modeling tools while taking advantage of the most recent advances in load balancing and scalable solution algorithms. Evolving interfaces are represented using the level-set method and the evolution equations time integrated using a Semi-Lagrangian approach [1]. The computational meshes used are quad-trees (2D) and oct-trees (3D), constructed such that grid refinement is localized to regions near the surface interfaces. As the interface evolves, the mesh is dynamically reconstructed as needed for the grid to remain fine only around the interface. For parallel computation, a domain decomposition scheme with dynamic load balancing is used to distribute the computational work across processors. A ballistic transport model is employed to solve for the fluxes incident on each of the surface elements. Surface chemistry is computed by either coupling to the CHEMKIN software [2] or by providing user defined subroutines. This report describes the theoretical underpinnings, methods, and practical use instruction of the ChISELS 1.0 computer code.

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TYPE SAND Report YEAR 2006
OSTIDOI

Report on ASC project degradation of organic materials

Lo, Chi S.; Thompson, Aidan P.; Grest, Gary S.

Using molecular dynamics simulations, a constitutive model for the chemical aging of polymer networks was developed. This model incorporates the effects on the stress from the chemical crosslinks and the physical entanglements. The independent network hypothesis has been modified to account for the stress transfer between networks due to crosslinking and scission in strained states. This model was implemented in the finite element code Adagio and validated through comparison with experiment. Stress relaxation data was used to deduce crosslinking history and the resulting history was used to predict permanent set. The permanent set predictions agree quantitatively with experiment.

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TYPE SAND Report YEAR 2006
OSTIDOI

Sandia National Laboratories Advanced Simulation and Computing (ASC) software quality plan part 2 mappings for the ASC software quality engineering practices, version 2.0

Boucheron, Edward A.; Sturtevant, Judy E.; Drake, Richard R.; Edwards, Harold C.; Forsythe, Christi A.; Heaphy, Robert T.; Hodges, Ann L.; Minana, Molly A.; Pavlakos, Constantine P.; Schofield, Joseph R.

The purpose of the Sandia National Laboratories Advanced Simulation and Computing (ASC) Software Quality Plan is to clearly identify the practices that are the basis for continually improving the quality of ASC software products. The plan defines the ASC program software quality practices and provides mappings of these practices to Sandia Corporate Requirements CPR001.3.2 and CPR001.3.6 and to a Department of Energy document, ''ASCI Software Quality Engineering: Goals, Principles, and Guidelines''. This document also identifies ASC management and software project teams' responsibilities in implementing the software quality practices and in assessing progress towards achieving their software quality goals.

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TYPE SAND Report YEAR 2006
OSTIDOI

Sandia National Laboratories Advanced Simulation and Computing (ASC) software quality plan. Part 1: ASC software quality engineering practices, Version 2.0

Drake, Richard R.; Sturtevant, Judy E.; Boucheron, Edward A.; Edwards, Harold C.; Minana, Molly A.; Forsythe, Christi A.; Heaphy, Robert T.; Hodges, Ann L.; Pavlakos, Constantine P.; Schofield, Joseph R.

The purpose of the Sandia National Laboratories Advanced Simulation and Computing (ASC) Software Quality Plan is to clearly identify the practices that are the basis for continually improving the quality of ASC software products. The plan defines the ASC program software quality practices and provides mappings of these practices to Sandia Corporate Requirements CPR 1.3.2 and 1.3.6 and to a Department of Energy document, ASCI Software Quality Engineering: Goals, Principles, and Guidelines. This document also identifies ASC management and software project teams responsibilities in implementing the software quality practices and in assessing progress towards achieving their software quality goals.

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TYPE SAND Report YEAR 2006
OSTIDOI
Results 9201–9250 of 9,998
Results 9201–9250 of 9,998