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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; 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; 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
DOIOSTI

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

Musson, Lawrence C.; 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
DOIOSTI

Report on ASC project degradation of organic materials

Lo, Chi S.; Thompson, A.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
DOIOSTI

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, Judith E.; Drake, Richard R.; Edwards, Harold C.; Forsythe, Christi A.; Heaphy, Robert T.; Hodges, Ann L.; Minana, Molly A.; Pavlakos, Constantine; 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
DOIOSTI

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, Judith E.; Boucheron, Edward A.; Edwards, Harold C.; Minana, Molly A.; Forsythe, Christi A.; Heaphy, Robert T.; Hodges, Ann L.; Pavlakos, Constantine; 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
DOIOSTI

QCS : a system for querying, clustering, and summarizing documents

Dunlavy, Daniel M.

Information retrieval systems consist of many complicated components. Research and development of such systems is often hampered by the difficulty in evaluating how each particular component would behave across multiple systems. We present a novel hybrid information retrieval system--the Query, Cluster, Summarize (QCS) system--which is portable, modular, and permits experimentation with different instantiations of each of the constituent text analysis components. Most importantly, the combination of the three types of components in the QCS design improves retrievals by providing users more focused information organized by topic. We demonstrate the improved performance by a series of experiments using standard test sets from the Document Understanding Conferences (DUC) along with the best known automatic metric for summarization system evaluation, ROUGE. Although the DUC data and evaluations were originally designed to test multidocument summarization, we developed a framework to extend it to the task of evaluation for each of the three components: query, clustering, and summarization. Under this framework, we then demonstrate that the QCS system (end-to-end) achieves performance as good as or better than the best summarization engines. Given a query, QCS retrieves relevant documents, separates the retrieved documents into topic clusters, and creates a single summary for each cluster. In the current implementation, Latent Semantic Indexing is used for retrieval, generalized spherical k-means is used for the document clustering, and a method coupling sentence ''trimming'', and a hidden Markov model, followed by a pivoted QR decomposition, is used to create a single extract summary for each cluster. The user interface is designed to provide access to detailed information in a compact and useful format. Our system demonstrates the feasibility of assembling an effective IR system from existing software libraries, the usefulness of the modularity of the design, and the value of this particular combination of modules.

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TYPE SAND Report YEAR 2006
DOIOSTI

First-principles approach to the charge-transport characteristics of monolayer molecular-electronics devices: Application to hexanedithiolate devices

Physical Review B - Condensed Matter and Materials Physics

Kim, Yong H.; Tahir-Kheli, Jamil; Schultz, Peter A.; Goddard, William A.

We report on the development of an accurate first-principles computational scheme for the charge transport characteristics of molecular monolayer junctions and its application to hexanedithiolate (C6DT) devices. Starting from the Gaussian basis set density-functional calculations of a junction model in the slab geometry and corresponding two bulk electrodes, we obtain the transmission function using the matrix Green's function method and analyze the nature of transmission channels via atomic projected density of states. Within the developed formalism, by treating isolated molecules with the supercell approach, we can investigate the current-voltage characteristics of single and parallel molecular wires in a consistent manner. For the case of single C6DT molecules stretched between Au(111) electrodes, we obtain reasonable quantitative agreement of computed conductance with a recent scanning tunneling microscope experiment result. Comparing the charge transport properties of C6DT single molecules and their monolayer counterparts in the stretched and tilted geometries, we find that the effect of intermolecular coupling and molecule tilting on the charge transport characteristics is negligible in these devices. We contrast this behavior to that of the π -conjugated biphenyldithiolate devices we have previously considered and discuss the relative importance of molecular cores and molecule-electrode contacts for the charge transport in those devices. © 2006 The American Physical Society.

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TYPE Journal Article YEAR 2006
ScopusOSTI

Parallel parameter study of the Wigner-Poisson equations for RTDs

Computers and Mathematics with Applications

Lasater, M.S.; Kelley, C.T.; Salinger, Andrew G.; Woolard, D.L.; Zhao, P.

We will discuss a parametric study of the solution of the Wigner-Poisson equations for resonant tunneling diodes. These structures exhibit self-sustaining oscillations in certain operating regimes. We will describe the engineering consequences of our study and how it is a significant advance from some previous work, which used much coarser grids. We use LOCA and other packages in the Trilinos framework from Sandia National Laboratory to enable efficient parallelization of the solution methods and to perform bifurcation analysis of this model. We report on the parallel efficiency and scalability of our implementation. © 2006 Elsevier Ltd. All rights reserved.

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TYPE Journal Article YEAR 2006
ScopusOSTI
Results 9201–9300 of 9,998
Results 9201–9300 of 9,998