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The complexstep derivative approximation
 ACM Transactions on Mathematical Software
"... The complexstep derivative approximation and its application to numerical algorithms are presented. Improvements to the basic method are suggested that further increase its accuracy and robustness and unveil the connection to algorithmic differentiation theory. A general procedure for the implement ..."
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Cited by 31 (4 self)
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The complexstep derivative approximation and its application to numerical algorithms are presented. Improvements to the basic method are suggested that further increase its accuracy and robustness and unveil the connection to algorithmic differentiation theory. A general procedure for the implementation of the complexstep method is described in detail and a script is developed that automates its implementation. Automatic implementations of the complexstep method for Fortran and C/C++ are presented and compared to existing algorithmic differentiation tools. The complexstep method is tested in two large multidisciplinary solvers and the resulting sensitivities are compared to results given by finite differences. The resulting sensitivities are shown to be as accurate as the analyses. Accuracy, robustness, ease of implementation and maintainability make these complexstep derivative approximation tools very attractive options for sensitivity analysis.
Algorithm Developments for Discrete Adjoint Methods
, 2001
"... This paper presents a number of algorithm developments for adjoint methods using the `discrete' approach in which the discretisation of the nonlinear equations is linearised and the resulting matrix is then transposed ..."
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Cited by 25 (7 self)
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This paper presents a number of algorithm developments for adjoint methods using the `discrete' approach in which the discretisation of the nonlinear equations is linearised and the resulting matrix is then transposed
Multidisciplinary Design Optimization Techniques: Implications and Opportunities for Fluid Dynamics Research
 JAROSLAW SOBIESZCZANSKISOBIESKI AND RAPHAEL T. HAFTKA ”MULTIDISCIPLINARY AEROSPACE DESIGN OPTIMIZATION: SURVEY OF RECENT DEVELOPMENTS,” 34TH AIAA AEROSPACE SCIENCES MEETING AND EXHIBIT
, 1999
"... A challenge for the fluid dynamics community is to adapt to and exploit the trend towards greater multidisciplinary focus in research and technology. The past decade has witnessed substantial growth in the research field of Multidisciplinary Design Optimization (MDO). MDO is a methodology for the de ..."
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Cited by 22 (0 self)
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A challenge for the fluid dynamics community is to adapt to and exploit the trend towards greater multidisciplinary focus in research and technology. The past decade has witnessed substantial growth in the research field of Multidisciplinary Design Optimization (MDO). MDO is a methodology for the design of complex engineering systems and subsystems that coherently exploits the synergism of mutually interacting phenomena. As evidenced by the papers, which appear in the biannual AIAA/USAF/NASA/ISSMO Symposia on Multidisciplinary Analysis and Optimization, the MDO technical community focuses on vehicle and system design issues. This paper provides an overview of the MDO technology field from a fluid dynamics perspective, giving emphasis to suggestions of specific applications of recent MDO technologies that can enhance fluid dynamics research itself across the spectrum, from basic flow physics to full configuration aerodynamics.
Computational Fluid Dynamics for Aerodynamic Design: Its . . .
 Its Current and Future Impact, AIAA 20010538, 39th AIAA Aerospace Sciences Meeting & Exhibit
, 2001
"... This paper discusses the role that computational fluid dynamics plays in the design of aircraft. An overview of the design process is provided, covering some of the typical decisions that a design team addresses within a multidisciplinary environment. On a very regular basis tradeoffs between disc ..."
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Cited by 15 (7 self)
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This paper discusses the role that computational fluid dynamics plays in the design of aircraft. An overview of the design process is provided, covering some of the typical decisions that a design team addresses within a multidisciplinary environment. On a very regular basis tradeoffs between disciplines have to be made where a set of conflicting requirements exist. Within an aircraft development project, we focus on the aerodynamic design problem and review how this process has been advanced, first with the improving capabilities of traditional computational fluid dynamics analyses, and then with aerodynamic optimizations based on these increasingly accurate methods. The optimization method of the present work is based on the use of the adjoint of the flow equations to compute the gradient of the cost function. Then, we use this gradient to navigate the design space in an efficient manner to find a local minimum. The computational costs of the present method are compared with that of other approaches to aerodynamic optimization. A brief discussion regarding the formulation of a continuous adjoint, as opposed to a discrete one, is also included. Two case studies are provided...
The Connection Between The ComplexStep Derivative Approximation And Algorithmic Differentiation
, 2001
"... This paper presents improvements to the complexstep derivative approximation method which increase its accuracy and robustness. These improvements unveil the connection to algorithmic differentiation theory. The choice between these two methods then hinges on a tradeoff between ease of implementati ..."
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Cited by 13 (5 self)
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This paper presents improvements to the complexstep derivative approximation method which increase its accuracy and robustness. These improvements unveil the connection to algorithmic differentiation theory. The choice between these two methods then hinges on a tradeoff between ease of implementation and execution efficiency. Automatic implementations for Fortran and C/C++ are presented and their relative merits are discussed. These new methods were successfully implemented in two very large multidisciplinary programs and the resulting sensitivities are shown to be as accurate as the analyses. Accuracy and ease of implementation make these tools very attractive options for sensitivity analysis.
Adjoint Code Developments Using the Exact Discrete Approach
 AIAA PAPER
, 2001
"... This paper presents a number of algorithm developments for adjoint methods using the `discrete' approach in which the discretisation of the nonlinear equations is linearised and the resulting matrix is then transposed. With a new iterative procedure for solving the adjoint equations, exact n ..."
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Cited by 10 (4 self)
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This paper presents a number of algorithm developments for adjoint methods using the `discrete' approach in which the discretisation of the nonlinear equations is linearised and the resulting matrix is then transposed. With a new iterative procedure for solving the adjoint equations, exact numerical equivalence is maintained between the linear and adjoint discretisations. The incorporation of strong boundary conditions within the discrete approach is discussed, as well as a new application of adjoint methods to linear unsteady flow in turbomachinery
Aerodynamic Design Sensitivities on an Unstructured Mesh Using the NavierStokes Equations and a Discrete Adjoint Formulation
, 1998
"... A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the threedimensional Reynoldsaveraged NavierStokes equations coupled with a oneequation turbulence model. A discussion of the numerical implementation of ..."
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Cited by 10 (3 self)
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A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the threedimensional Reynoldsaveraged NavierStokes equations coupled with a oneequation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated, and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences and a complexvariable approach. Several simplifying approximations to the complete linearization of the residual are also presented. A firstorder approximation to the dependent variables is implemented in the adjoint and design equations, and the effect of a “frozen ” eddy viscosity and neglecting mesh sensitivity terms is also examined. The resulting derivatives from these approximations are all shown to be inaccurate and often of incorrect sign. However, a partiallyconverged adjoint solution is shown to be sufficient for computing accurate sensitivity derivatives, yielding a potentially large cost savings in the design process. The convergence rate of the adjoint solver is compared to that of the flow solver. For inviscid adjoint solutions, the cost is roughly one to four times that of a flow solution, whereas for turbulent computations, this ratio can reach as high as ten. Sample optimizations are
Efficient aerodynamic shape optimization
 AIAA Paper
, 2004
"... Since the present author first became involved in computational fluid dynamics, around 1970, the landscape has changed dramatically. At that time, panel methods had just come into use, and the world’s fastest super computer, the Control data 6600, had only 131000 words of memory (about 1 megabyte). ..."
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Cited by 5 (4 self)
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Since the present author first became involved in computational fluid dynamics, around 1970, the landscape has changed dramatically. At that time, panel methods had just come into use, and the world’s fastest super computer, the Control data 6600, had only 131000 words of memory (about 1 megabyte). Prior to the breakthrough of Murman and Cole [1970], no viable algorithms for computing transonic flow with shock
Automatic Differentiation and Sensitivity Analysis Methods for Computational Fluid Dynamics
 QUB SCHOOL OF AERONAUTICAL ENGINEERING
, 2003
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