Publications

Bartlett, Roscoe B.

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Bartlett, Roscoe B.

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Bartlett, Roscoe B.

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Bartlett, Roscoe B.

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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.

Bartlett, Roscoe B.

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Bartlett, Roscoe B.

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Bartlett, Roscoe B.

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Bartlett, Roscoe B.

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Bartlett, Roscoe B.; Long, Kevin R.

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Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Bartlett, Roscoe B.; Gay, David M.; Phipps, Eric T.

We discuss computing first derivatives for models based on elements, such as large-scale finite-element PDE discretizations, implemented in the C++ programming language. We use a hybrid technique of automatic differentiation (AD) and manual assembly, with local element-level derivatives computed via AD and manually summed into the global derivative. C++ templating and operator overloading work well for both forward- and reverse-mode derivative computations. We found that AD derivative computations compared favorably in time to finite differencing for a scalable finite-element discretization of a convection-diffusion problem in two dimensions. © Springer-Verlag Berlin Heidelberg 2006.

Bartlett, Roscoe B.; Collis, Samuel S.; Keiter, Eric R.; Ober, Curtis C.

Sensitivity analysis is critically important to numerous analysis algorithms, including large scale optimization, uncertainty quantification,reduced order modeling, and error estimation. Our research focused on developing tools, algorithms and standard interfaces to facilitate the implementation of sensitivity type analysis into existing code and equally important, the work was focused on ways to increase the visibility of sensitivity analysis. We attempt to accomplish the first objective through the development of hybrid automatic differentiation tools, standard linear algebra interfaces for numerical algorithms, time domain decomposition algorithms and two level Newton methods. We attempt to accomplish the second goal by presenting the results of several case studies in which direct sensitivities and adjoint methods have been effectively applied, in addition to an investigation of h-p adaptivity using adjoint based a posteriori error estimation. A mathematical overview is provided of direct sensitivities and adjoint methods for both steady state and transient simulations. Two case studies are presented to demonstrate the utility of these methods. A direct sensitivity method is implemented to solve a source inversion problem for steady state internal flows subject to convection diffusion. Real time performance is achieved using novel decomposition into offline and online calculations. Adjoint methods are used to reconstruct initial conditions of a contamination event in an external flow. We demonstrate an adjoint based transient solution. In addition, we investigated time domain decomposition algorithms in an attempt to improve the efficiency of transient simulations. Because derivative calculations are at the root of sensitivity calculations, we have developed hybrid automatic differentiation methods and implemented this approach for shape optimization for gas dynamics using the Euler equations. The hybrid automatic differentiation method was applied to a first order approximation of the Euler equations and used as a preconditioner. In comparison to other methods, the AD preconditioner showed better convergence behavior. Our ultimate target is to perform shape optimization and hp adaptivity using adjoint formulations in the Premo compressible fluid flow simulator. A mathematical formulation for mixed-level simulation algorithms has been developed where different physics interact at potentially different spatial resolutions in a single domain. To minimize the implementation effort, explicit solution methods can be considered, however, implicit methods are preferred if computational efficiency is of high priority. We present the use of a partial elimination nonlinear solver technique to solve these mixed level problems and show how these formulation are closely coupled to intrusive optimization approaches and sensitivity analyses. Production codes are typically not designed for sensitivity analysis or large scale optimization. The implementation of our optimization libraries into multiple production simulation codes in which each code has their own linear algebra interface becomes an intractable problem. In an attempt to streamline this task, we have developed a standard interface between the numerical algorithm (such as optimization) and the underlying linear algebra. These interfaces (TSFCore and TSFCoreNonlin) have been adopted by the Trilinos framework and the goal is to promote the use of these interfaces especially with new developments. Finally, an adjoint based a posteriori error estimator has been developed for discontinuous Galerkin discretization of Poisson's equation. The goal is to investigate other ways to leverage the adjoint calculations and we show how the convergence of the forward problem can be improved by adapting the grid using adjoint-based error estimates. Error estimation is usually conducted with continuous adjoints but if discrete adjoints are available it may be possible to reuse the discrete version for error estimation. We investigate the advantages and disadvantages of continuous and discrete adjoints through a simple example.

Bartlett, Roscoe B.

Dynamic memory management in C++ is one of the most common areas of difficulty and errors for amateur and expert C++ developers alike. The improper use of operator new and operator delete is arguably the most common cause of incorrect program behavior and segmentation faults in C++ programs. Here we introduce a templated concrete C++ class Teuchos::RefCountPtr<>, which is part of the Trilinos tools package Teuchos, that combines the concepts of smart pointers and reference counting to build a low-overhead but effective tool for simplifying dynamic memory management in C++. We discuss why the use of raw pointers for memory management, managed through explicit calls to operator new and operator delete, is so difficult to accomplish without making mistakes and how programs that use raw pointers for memory management can easily be modified to use RefCountPtr<>. In addition, explicit calls to operator delete is fragile and results in memory leaks in the presents of C++ exceptions. In its most basic usage, RefCountPtr<> automatically determines when operator delete should be called to free an object allocated with operator new and is not fragile in the presents of exceptions. The class also supports more sophisticated use cases as well. This document describes just the most basic usage of RefCountPtr<> to allow developers to get started using it right away. However, more detailed information on the design and advanced features of RefCountPtr<> is provided by the companion document 'Teuchos::RefCountPtr : The Trilinos Smart Reference-Counted Pointer Class for (Almost) Automatic Dynamic Memory Management in C++'.

Shadid, John N.; van Bloemen Waanders, Bart G.; Bartlett, Roscoe B.

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Heroux, Michael A.; Kolda, Tamara G.; Long, Kevin R.; Hoekstra, Robert J.; Pawlowski, Roger P.; Phipps, Eric T.; Salinger, Andrew G.; Williams, Alan B.; Heroux, Michael A.; Hu, Jonathan J.; Lehoucq, Richard B.; Thornquist, Heidi K.; Tuminaro, Raymond S.; Willenbring, James M.; Bartlett, Roscoe B.; Howle, Victoria E.

The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries. In particular, our goal is to develop parallel solver algorithms and libraries within an object-oriented software framework for the solution of large-scale, complex multi-physics engineering and scientific applications. Our emphasis is on developing robust, scalable algorithms in a software framework, using abstract interfaces for flexible interoperability of components while providing a full-featured set of concrete classes that implement all abstract interfaces. Trilinos uses a two-level software structure designed around collections of packages. A Trilinos package is an integral unit usually developed by a small team of experts in a particular algorithms area such as algebraic preconditioners, nonlinear solvers, etc. Packages exist underneath the Trilinos top level, which provides a common look-and-feel, including configuration, documentation, licensing, and bug-tracking. Trilinos packages are primarily written in C++, but provide some C and Fortran user interface support. We provide an open architecture that allows easy integration with other solver packages and we deliver our software to the outside community via the Gnu Lesser General Public License (LGPL). This report provides an overview of Trilinos, discussing the objectives, history, current development and future plans of the project.

van Bloemen Waanders, Bart G.; van Bloemen Waanders, Bart G.; Bartlett, Roscoe B.

Increasing concerns for the security of the national infrastructure have led to a growing need for improved management and control of municipal water networks. To deal with this issue, optimization offers a general and extremely effective method to identify (possibly harmful) disturbances, assess the current state of the network, and determine operating decisions that meet network requirements and lead to optimal performance. This paper details an optimization strategy for the identification of source disturbances in the network. Here we consider the source inversion problem modeled as a nonlinear programming problem. Dynamic behavior of municipal water networks is simulated using EPANET. This approach allows for a widely accepted, general purpose user interface. For the source inversion problem, flows and concentrations of the network will be reconciled and unknown sources will be determined at network nodes. Moreover, intrusive optimization and sensitivity analysis techniques are identified to assess the influence of various parameters and models in the network in a computational efficient manner. A number of numerical comparisons are made to demonstrate the effectiveness of various optimization approaches.

Proposed for publication in the ACM Transactions on Mathematical Software journal.

Bartlett, Roscoe B.; Bartlett, Roscoe B.; van Bloemen Waanders, Bart G.; Heroux, Michael A.

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van Bloemen Waanders, Bart G.; Bartlett, Roscoe B.; Long, Kevin R.; Boggs, Paul T.; Salinger, Andrew G.

Three years of large-scale PDE-constrained optimization research and development are summarized in this report. We have developed an optimization framework for 3 levels of SAND optimization and developed a powerful PDE prototyping tool. The optimization algorithms have been interfaced and tested on CVD problems using a chemically reacting fluid flow simulator resulting in an order of magnitude reduction in compute time over a black box method. Sandia's simulation environment is reviewed by characterizing each discipline and identifying a possible target level of optimization. Because SAND algorithms are difficult to test on actual production codes, a symbolic simulator (Sundance) was developed and interfaced with a reduced-space sequential quadratic programming framework (rSQP++) to provide a PDE prototyping environment. The power of Sundance/rSQP++ is demonstrated by applying optimization to a series of different PDE-based problems. In addition, we show the merits of SAND methods by comparing seven levels of optimization for a source-inversion problem using Sundance and rSQP++. Algorithmic results are discussed for hierarchical control methods. The design of an interior point quadratic programming solver is presented.