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13
Adjoint sensitivity analysis for differentialalgebraic equations: algorithms and software
, 2002
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Halo Orbit Mission Correction Maneuvers Using Optimal Control
 Automatica
, 2000
"... This paper addresses the computation of the required trajectory correction maneuvers #TCM# for a halo orbit space mission to compensate for the launch velocity errors introduced by inaccuracies of the launchvehicle. By combining dynamical systems theory with optimal control techniques, we are abl ..."
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Cited by 11 (4 self)
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This paper addresses the computation of the required trajectory correction maneuvers #TCM# for a halo orbit space mission to compensate for the launch velocity errors introduced by inaccuracies of the launchvehicle. By combining dynamical systems theory with optimal control techniques, we are able to provide a compelling portrait of the complex landscape of the trajectory design space. This approach enables automation of the analysis to perform parametric studies that simply were not available to mission designers a few years ago, suchashow the magnitude of the errors and the timing of the #rst trajectory correction maneuver a#ects the correction #V . The impetus for combining dynamical systems theory and optimal control in this problem arises from design issues for the Genesis Discovery mission being developed for NASA by the Jet Propulsion Laboratory. 1 Introduction and Background 1.1 The Genesis Mission Genesis is a solar wind sample return mission #see Lo et al., #199...
Integrating Automatic Differentiation with ObjectOriented Toolkits for HighPerformance Scientific Computing
, 2000
"... Often the most robust and efficient algorithms for the solution of largescale problems involving nonlinear PDEs and optimization require the computation of derivative quantities. We examine the use of automatic differentiation (AD) to provide code for computing first and second derivatives in c ..."
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Cited by 4 (1 self)
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Often the most robust and efficient algorithms for the solution of largescale problems involving nonlinear PDEs and optimization require the computation of derivative quantities. We examine the use of automatic differentiation (AD) to provide code for computing first and second derivatives in conjunction with two parallel numerical toolkits, the Portable, Extensible Toolkit for Scientific Computing (PETSc) and the Toolkit for Advanced Optimization (TAO). We discuss how the use of mathematical abstractions for vectors and matrices in these libraries facilitates the use of AD to automatically generate derivative codes and present performance data demonstrating the suitability of this approach. 1 Introduction As the complexity of advanced computational science applications has increased, the use of objectoriented software methods for the development of both applications and numerical toolkits has also increased. The migration toward this approach can be attributed in part to ...
Sensitivity Analysis Using Parallel ODE Solvers and Automatic Differentiation in C: SensPVODE and ADIC
, 2000
"... PVODE is a highperformance ordinary differential equation solver for the types of initial value problems (IVPs) that arise in largescale computational simulations. Often, one wants to compute sensitivities with respect to certain parameters in the IVP. We discuss the use of automatic different ..."
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Cited by 4 (1 self)
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PVODE is a highperformance ordinary differential equation solver for the types of initial value problems (IVPs) that arise in largescale computational simulations. Often, one wants to compute sensitivities with respect to certain parameters in the IVP. We discuss the use of automatic differentiation (AD) to compute these sensitivities in the context of PVODE. Results on a simple test problem indicate that the use of ADgenerated derivative code can reduce the time to solution over finite difference approximations.
Adaptive Algorithms for Optimal Control of TimeDependent Partial DifferentialAlgebraic Equation Systems
"... This paper describes an adaptive algorithm for optimal control of timedependent partial differential algebraic equation (PDAE) systems. A direct method based on a modified multiple shooting type technique and sequential quadratic programming (SQP) is used for solving the optimal control problem, ..."
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Cited by 3 (0 self)
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This paper describes an adaptive algorithm for optimal control of timedependent partial differential algebraic equation (PDAE) systems. A direct method based on a modified multiple shooting type technique and sequential quadratic programming (SQP) is used for solving the optimal control problem, while an adaptive mesh refinement (AMR) algorithm is employed to dynamically adapt the spatial integration mesh. Issues of coupling the AMR solver to the optimization algorithm are addressed. For timedependent PDAEs which can benefit from the use of an adaptive mesh, the resulting method is shown to be highly efficient.
Deriving user interface requirements from densely interleaved scientific computing applications
 IEEE, 15th Automated Software Engineering Conference
, 2003
"... Deriving user interface requirements is a key step in user interface generation and maintenance. For single purpose numeric routines user interface requirements are relatively simple to derive. However, general numeric packages, which are solvers for entire classes of problems, are densely interleav ..."
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Cited by 2 (2 self)
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Deriving user interface requirements is a key step in user interface generation and maintenance. For single purpose numeric routines user interface requirements are relatively simple to derive. However, general numeric packages, which are solvers for entire classes of problems, are densely interleaved with strands shared and mixed among user options. This complexity forms a significant barrier to the derivation of user interface requirements and therefore to user interface generation and maintenance. Our methodology uses a graph representation to find potential user decision points implied by the control structure of the code. This graph is then iteratively refined to form a Decision Point Diagram, a state machine representation of all possible user traversals through a user interface for the underlying code.
Digital Filter Stepsize Control of DASPK and its Effect on Control Optimization Performance
 M.SC. THESIS, UCSB
, 2004
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Automated User Interface Requirements Discovery for Scientific Computing
 IN 11TH IEEE CONFERENCE ON REQUIREMENTS ENGINEERING
, 2003
"... In this paper we introduce a method for determining user interface requirements for scientific computing codes that use the most flexible method of user input; compiledin input. Compiledin input means that the user writes subroutines and drivers which describe the problem to be solved. These routi ..."
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Cited by 1 (1 self)
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In this paper we introduce a method for determining user interface requirements for scientific computing codes that use the most flexible method of user input; compiledin input. Compiledin input means that the user writes subroutines and drivers which describe the problem to be solved. These routines are compiled together with the application to form a working program to solve the problem the user has described. This method of input gives the user the maximum flexibility of an entire programming language to describe the problem and allows unlimited nesting and combination of codes to form larger, more complex applications. Our methodology uses a graph representation to find potential user decision points implied by the control structure of the code. This graph is then iteratively refined to form a Decision Point Diagram, a state machine representation of all possible user traversals through a user interface for the underlying code.
A Numerical Study of Transient Ignition in a Counterflow Nonpremixed MethaneAir Flame using Adaptive Time Integration
"... This paper presents a computational algorithm to predict highlytransient flame behavior in counterflow situations. The first objective of the paper is to extend the transient counterflow problem to incorporate some gasdynamic compressibility effects, yet retain the desirable similarity structure. B ..."
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This paper presents a computational algorithm to predict highlytransient flame behavior in counterflow situations. The first objective of the paper is to extend the transient counterflow problem to incorporate some gasdynamic compressibility effects, yet retain the desirable similarity structure. By relaxing assumptions in earlier formulations, the computational algorithms can deliver high accuracy even in periods of extremely rapid transients, like combustion ignition. The algorithms are demonstrated on twocombustionignition problems for methaneair, counterflow, nonpremixed flames. The first concerns the ignition transient in a steady strain field. The second concerns the effects of a highfrequency oscillatory strain field on the ignition process. The results reveal that, when the mean strain rate is near the steady ignition limit, the ignition process is highly sensitive to the details of the strainrate fluctuations.
Efficient Solution and Sensitivity Analysis of Partial DifferentialAlgebraic Equation Systems Modelling Corrosion Pit Initiation
"... A mathematical model based on transport and reaction equations describing initiation of pitting corrosion at a MnS sulfide inclusion in 0.1M NaCl electrolyte was used as a test problem for development of efficient numerical procedures for corrosion simulation and sensitivity analysis. The equations ..."
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A mathematical model based on transport and reaction equations describing initiation of pitting corrosion at a MnS sulfide inclusion in 0.1M NaCl electrolyte was used as a test problem for development of efficient numerical procedures for corrosion simulation and sensitivity analysis. The equations associated with the corrosion model were formulated using a reaction invariant approach, which resulted in a stiff index2 Partial DifferentialAlgebraic Equation (PDAE) system. The original PDAE system was regularized to yield a lower index PDAE system, for which we were able to formulate an effective preconditioner for use in the DASP K3.0 DAE solver. This approach was found to improve the efficiency of the Krylov iterative solver as well as to provide the parameter sensitivities with very little additional effort, in comparison with another method reported recently. In agreement with previous findings, the results obtained with this approach indicate that the model is most sensitive to the parameters associated with the heterogeneous dissolution of the sulfide inclusion.