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14
Optical tomography as a PDEconstrained optimisation problem
 Inverse Problems
, 2005
"... We report on the implementation of an augmented Lagrangian approach for solving the inverse problems in diffuse optical tomography (DOT). The forward model of light propagation is the radiative transport equation (RTE). The inverse problem is formulated as a minimization problem with the RTE being c ..."
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We report on the implementation of an augmented Lagrangian approach for solving the inverse problems in diffuse optical tomography (DOT). The forward model of light propagation is the radiative transport equation (RTE). The inverse problem is formulated as a minimization problem with the RTE being considered as an equality constraint on the set of ‘optical properties—radiance’ pairs. This approach allows the incorporation of the recently developed technique of PDEconstrained optimization, which has shown great promise in many applications that can be formulated as infinitedimensional optimization problems. Compared to the traditional unconstrained optimization approaches for optical tomographic imaging where one solves several forward and adjoint problems at each optimization iteration, the method proposed in this work solves the forward and inverse problems simultaneously. We found in initial studies, using synthetic data, that the image reconstruction time can typically be reduced by a factor of 10 to 30, which depends on a combination of noise level, regularization parameter, mesh size, initial guess, optical properties and system geometry. 1.
Inexactness issues in the LagrangeNewtonKrylovSchur method for PDEconstrained optimization
 LargeScale PDEConstrained Optimization, number 30 in Lecture
"... Abstract. In this article we present an outline of the LagrangeNewtonKrylovSchur (LNKS) method and we discuss how we can improve its work efficiency by carrying out certain computations inexactly, without compromising convergence. LNKS has been designed for PDEconstrained optimization problems. I ..."
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Abstract. In this article we present an outline of the LagrangeNewtonKrylovSchur (LNKS) method and we discuss how we can improve its work efficiency by carrying out certain computations inexactly, without compromising convergence. LNKS has been designed for PDEconstrained optimization problems. It solves the KarushKuhnTucker optimality conditions by a NewtonKrylov algorithm. Its key component is a preconditioner based on quasiNewton reduced space Sequential Quadratic Programming (QNRSQP) variants. LNKS combines the fastconvergence properties of a Newton method with the capability of preconditioned Krylov methods to solve very large linear systems. Nevertheless, even with good preconditioners, the solution of an optimization problem has a cost which is several times higher than the cost of the solution of the underlying PDE problem. To accelerate LNKS, its computational components are carried out inexactly: premature termination of iterative algorithms, inexact evaluation of gradients and Jacobians, approximate line searches. Naturally, several issues arise with respect to the tradeoffs between speed and robustness. 1
Parallel NewtonKrylov Methods For PDEConstrained Optimization
 In Proceedings of Supercomputing ’99
, 1999
"... . Large scale optimization of systems governed by partial differential equations (PDEs) is a frontier problem in scientific computation. The stateoftheart for solving such problems is reducedspace quasiNewton sequential quadratic programming (SQP) methods. These take full advantage of existing ..."
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. Large scale optimization of systems governed by partial differential equations (PDEs) is a frontier problem in scientific computation. The stateoftheart for solving such problems is reducedspace quasiNewton sequential quadratic programming (SQP) methods. These take full advantage of existing PDE solver technology and parallelize well. However, their algorithmic scalability is questionable; for certain problem classes they can be very slow to converge. In this paper we propose a fullspace NewtonKrylov SQP method that uses the reducedspace quasiNewton method as a preconditioner. The new method is fully parallelizable; exploits the structure of and available parallel algorithms for the PDE forward problem; and is quadratically convergent close to a local minimum. We restrict our attention to boundary value problems and we solve a model optimal flow control problem, with both Stokes and NavierStokes equations as constraints. Algorithmic comparisons, scalability results, and para...
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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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.
Topology optimization of creeping fluid flows using a Darcy–Stokes finite element
"... A new methodology is proposed for the topology optimization of fluid in Stokes flow. The binary design variable and noslip condition along the solid–fluid interface are regularized to allow for the use of continuous mathematical programming techniques. The regularization is achieved by treating the ..."
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A new methodology is proposed for the topology optimization of fluid in Stokes flow. The binary design variable and noslip condition along the solid–fluid interface are regularized to allow for the use of continuous mathematical programming techniques. The regularization is achieved by treating the solid phase of the topology as a porous medium with flow governed by Darcy’s law. Fluid flow throughout the design domain is then expressed as a single system of equations created by combining and scaling the Stokes and Darcy equations. The mixed formulation of the new Darcy–Stokes system is solved numerically using existing stabilized finite element methods for the individual flow problems. Convergence to the noslip condition is demonstrated by assigning a low permeability to solid phase and results suggest that auxiliary boundary conditions along the solid–fluid interface are not needed. The optimization objective considered is to minimize dissipated power and the technique is used to solve examples previously examined in literature. The advantages of the Darcy–Stokes approach include that it uses existing stabilization techniques to solve the finite element problem, it produces 0–1 (void–solid) topologies (i.e. there are no regions of artificial material), and that it can potentially be used to optimize the layout of a microscopically porous material. Copyright 2005 John Wiley & Sons, Ltd. KEY WORDS: topology optimization; stabilized finite element methods; porous media; coupled flow;
unknown title
, 2004
"... Adjoint sensitivity analysis for timedependent partial differential equations with adaptive mesh refinement q ..."
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Adjoint sensitivity analysis for timedependent partial differential equations with adaptive mesh refinement q
Adjoint sensitivity analysis for differentialalgebraic equations: The adjoint DAE system and its numerical solution
 SIAM J. Sci. Comput
, 2003
"... Sensitivity analysis generates essential information for model development, design optimization, parameter estimation, optimal control, model reduction and experimental design. In this paper we describe the forward and adjoint methods for sensitivity analysis, and outline some of our recent work on ..."
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Sensitivity analysis generates essential information for model development, design optimization, parameter estimation, optimal control, model reduction and experimental design. In this paper we describe the forward and adjoint methods for sensitivity analysis, and outline some of our recent work on theory, algorithms and software for sensitivity analysis of differentialalgebraic equation (DAE) and timedependent partial differential equation (PDE) systems. 1
Integrated Software Infrastructure Centers Proposing Organization: Old Dominion University
"... No use of human subjects in proposed project No use of vertebrate animals in proposed project ..."
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No use of human subjects in proposed project No use of vertebrate animals in proposed project
Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/cfg.465 Conference Paper
, 2005
"... glimpse of the Brassica genome based on comparative genome analysis with ..."
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