Massively parallel aerodynamic shape optimization

Orozco, Carlos E.; Ghattas, Omar

doi:10.1016/0956-0521(92)90116-z

Cited by 20 publications

(12 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Problems of this kind arise in the description of a multitude of scientific and engineering applications including optimal design, control, and parameter identification [8]. Examples of PDE-constrained optimization problems arise in aerodynamics [30,36], mathematical finance [10,15,16], medicine [4,26], and geophysics and environmental engineering [2,1,27]. PDE-constrained optimization problems are infinite-dimensional and often ill-posed in nature, and their discretization invariably leads to systems of equations that are typically very large and difficult to solve.…”

Section: Introductionmentioning

confidence: 99%

A preconditioning technique for a class of PDE-constrained optimization problems

Benzi

Haber

Taralli³

2011

Adv Comput Math

View full text Add to dashboard Cite

We investigate the use of a preconditioning technique for solving linear systems of saddle point type arising from the application of an inexact Gauss-Newton scheme to PDE-constrained optimization problems with a hyperbolic constraint. The preconditioner is of block triangular form and involves diagonal perturbations of the (approximate) Hessian to insure nonsingularity and an approximate Schur complement. We establish some properties of the preconditioned saddle point systems and we present the results of numerical experiments illustrating the performance of the preconditioner on a model problem motivated by image registration.

show abstract

Section: Introductionmentioning

confidence: 99%

A preconditioning technique for a class of PDE-constrained optimization problems

Benzi

Haber

Taralli³

2011

Adv Comput Math

View full text Add to dashboard Cite

show abstract

“…A promising approach to automate the geometric aspects of shape optimization for arbitrary geometries is the skeletal method of [17]. With regard to the difficulties induced by the large number of design and state variables inherent in three dimensions, a framework for addressing these problems is contained within the parallel reduced SQP method of [14]. We intend to incorporate aspects of these approaches into our continuation-SQP algorithm.…”

Section: Discussionmentioning

confidence: 99%

“…The implicit function theorem is invoked to find gradients of objective and constraint functions. In the future we will consider methods that retain the state equations as equality constraints, thereby obviating the need for flow solution at each iteration [14]. An SQP method is used to solve the optimization problem.…”

Section: Numerical Optimizationmentioning

confidence: 99%

Shape optimization of Navier-Stokes flows with application to optimal design of artificial heart components

He¹,

Ghattas²,

Antaki³

et al. 1994

5th Symposium on Multidisciplinary Analysis and Optimization

View full text Add to dashboard Cite

We consider the problem of shape optimization of systems governed by the stationary incompressible Navier-Stokes equations under flow and geometric constraints. Our motivation stems from the problem of optimal design of artificial heart components. An continuation-SQP algorithm is developed to efficiently couple Newton-based optimization and flow solution. The main feature of the algorithm is to decompose the optimization problem into a sequence of subproblems characterized by increasing Reynolds numbers, and then apply continuation schemes on the design field, Hessian matrix, Lagrange multipliers, and flowfield. As an application we consider the optimum design of the shape of a two dimensional tube-a simplification of a blood flow cannula that is a component of an artificial heart. Representative numerical results show a factor of four improvement in efficiency over a standard SQP algorithm.

show abstract

“…Optimization problems, constraints with partial differential equation (PDE), arise in many areas such as mathematical finance [2,3,4], aerodynamics [13,15], environmental engineering [11] and medicine [1,10] and generally are infinite dimensional, large and complex. In order to solve a PDE-constrained optimization problem, the question about should I first discretize the optimization problem and then solve the discretized optimization problem (DO), or should first I optimize the continuous problem and obtain a set of equations to discretize (OD), is not avoidable.…”

Section: Introductionmentioning

confidence: 99%

“…Thus (13) and (14) together are aquivalent to (11) and (12). In order to solve this minimization problem, one way is considering the Lagrangian…”

mentioning

confidence: 99%

Convergence Analysis Of Gradient Based Iterative Algorithm For Solving Pde Constrained Optimization Problems

Naseri¹,

Malek²

2014

J. Math. Computer Sci.

View full text Add to dashboard Cite

In this paper, by considering distributed optimal control over a PDE, a gradient based iterative Algorithm is proposed for solving is proposed and analyzed. Galerkin finite element method is used for solving underlying PDE, then the adjoint base technique for derivative computation to implementation of the optimal control issue in preconditioned Newton's conjugate gradient method isused. The interface and connection between quadratic programming extracted from discretizing the problem and Newton's type method, as well as the convergence rate of the algorithm in each iteration is established.Updating control values at discretization points in each iteration yields optimal control of the problem, where the corresponding state values at these points approximate the desired function. Numerical experiments are presented for illustrating the theoretical results.

show abstract

Massively parallel aerodynamic shape optimization

Cited by 20 publications

References 20 publications

A preconditioning technique for a class of PDE-constrained optimization problems

A preconditioning technique for a class of PDE-constrained optimization problems

Shape optimization of Navier-Stokes flows with application to optimal design of artificial heart components

Convergence Analysis Of Gradient Based Iterative Algorithm For Solving Pde Constrained Optimization Problems

Contact Info

Product

Resources

About