Download or read book Approximate Hessian for Accelerated Convergence of Aerodynamic Shape Optimization Problems in an Adjoint based Framework written by Doug Shi-Dong and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "An approximation of the Hessian matrix is developed and used to accelerate the convergence of an adjoint-based aerodynamic shape optimization framework. Exact analytical formulations of the direct-direct, adjoint-direct, adjoint-adjoint, and direct-adjoint Hessian approaches are presented and the equivalence between the adjoint-adjoint and direct-adjoint formulations is demonstrated. An approximation of the Hessian is obtained from the analytical formulation by partially solving first-order sensitivities to reduce computational time, while neglecting second-order sensitivities to ease implementation. Error bounds on the resulting approximation are presented for the first-order sensitivities through perturbation analysis and eigenvalue analysis. The proposed method is first assessed using an inverse design pressure problem for a quasi-one-dimensional Euler flow. Additionally, three-dimensional inviscid transonic test cases are used to demonstrate the effectiveness of the method.Eigenvalue analysis of the Hessian for various test cases will seek to explain the resulting acceleration." --

Download or read book Analysis of the Hessian for Aeroelastic Optimization written by Eyal Arian and published by . This book was released on 1995 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Preconditioning Method for Shape Optimization Governed by the Euler Equations written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-08-09 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a classical aerodynamic shape optimization problem subject to the compressible Euler flow equations. The gradient of the cost functional with respect to the shape variables is derived with the adjoint method at the continuous level. The Hessian (second order derivative of the cost functional with respect to the shape variables) is approximated also at the continuous level, as first introduced by Arian and Ta'asan (1996). The approximation of the Hessian is used to approximate the Newton step which is essential to accelerate the numerical solution of the optimization problem. The design space is discretized in the maximum dimension, i.e., the location of each point on the intersection of the computational mesh with the airfoil is taken to be an independent design variable. We give numerical examples for 86 design variables in two different flow speeds and achieve an order of magnitude reduction in the cost functional at a computational effort of a full solution of the analysis partial differential equation (PDE). Arian, Eyal and Vatsa, Veer N. Langley Research Center NASA/CR-1998-206926, NAS 1.26:206926, ICASE-98-14 NAS1-19480; RTOP 505-90-52-01...

Download or read book Analysis of the Hessian for Aerodynamic Optimization written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-06-30 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we analyze inviscid aerodynamic shape optimization problems governed by the full potential and the Euler equations in two and three dimensions. The analysis indicates that minimization of pressure dependent cost functions results in Hessians whose eigenvalue distributions are identical for the full potential and the Euler equations. However the optimization problems in two and three dimensions are inherently different. While the two dimensional optimization problems are well-posed the three dimensional ones are ill-posed. Oscillations in the shape up to the smallest scale allowed by the design space can develop in the direction perpendicular to the flow, implying that a regularization is required. A natural choice of such a regularization is derived. The analysis also gives an estimate of the Hessian's condition number which implies that the problems at hand are ill-conditioned. Infinite dimensional approximations for the Hessians are constructed and preconditioners for gradient based methods are derived from these approximate Hessians. Arian, Eyal and Ta'asan, Shlomo Ames Research Center NAS1-19480...

Download or read book Adjoint Methods for Aerodynamic Shape Optimization written by Gábor Povorai and published by . This book was released on 2020 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: This master thesis investigated the applicability of the Hicks-Henne bump functions and Free-Form Deformation as shape deformation methods used for aerodynamic shape optimization by the adjoint method. In order to alleviate user effort in the setup of simulations and post-processing of results, a MatLab framework has been developed. This framework integrated shape definition, meshing, file management, flow solver and post-processing tools. The external tools were open-source software. to allow the use of arbitrary cell and processor core numbers. The computational fluid dynamics solver, SU2 was used to obtain direct flow and adjoint solutions and to perform shape deformations using the built in nonlinear constrained optimization function. Automatic mesh generation was done using GMSH. The thesis focused on inviscid and viscous 2D problems in the transonic and supersonic flow regimes. The definition of the initial aerodynamic shapes was done using the Class-Shape Transformation method. The test cases optimization problems with the NACA0012 airfoil as the initial airfoil for deformation, with drag reduction as the objective function. The test cases involved different constraints e.g. airfoil thickness, lift coefficient and pitching moment coefficient. Comparisons were made between the two methods in terms of performance in the minimization of the objective function. The results of the optimization problems were compared to reference airfoils from literature. Both deformation methods proved to be effective, clear superiority of one method over the other could not be shown.*****This master thesis investigated the applicability of the Hicks-Henne bump functions and Free-Form Deformation as shape deformation methods used for aerodynamic shape optimization by the adjoint method. In order to alleviate user effort in the setup of simulations and post-processing of results, a MatLab framework has been developed. This framework integrated shape definition, meshing, file manage

Download or read book An adjoint based shape optimization method for aerodynamic design written by Giampietro Carpentieri and published by . This book was released on 2009 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optimization and Computational Fluid Dynamics written by Dominique Thévenin and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical optimization of practical applications has been an issue of major importance for the last 10 years. It allows us to explore reliable non-trivial configurations, differing widely from all known solutions. The purpose of this book is to introduce the state-of-the-art concerning this issue and many complementary applications are presented.

Download or read book Engineering Design Optimization written by Joaquim R. R. A. Martins and published by Cambridge University Press. This book was released on 2021-11-18 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-semester graduate course on optimization in aerospace, civil, mechanical, electrical, and chemical engineering departments.

Download or read book Optimal Shape Design written by B. Kawohl and published by Springer Science & Business Media. This book was released on 2000-11-16 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal Shape Design is concerned with the optimization of some performance criterion dependent (besides the constraints of the problem) on the "shape" of some region. The main topics covered are: the optimal design of a geometrical object, for instance a wing, moving in a fluid; the optimal shape of a region (a harbor), given suitable constraints on the size of the entrance to the harbor, subject to incoming waves; the optimal design of some electrical device subject to constraints on the performance. The aim is to show that Optimal Shape Design, besides its interesting industrial applications, possesses nontrivial mathematical aspects. The main theoretical tools developed here are the homogenization method and domain variations in PDE. The style is mathematically rigorous, but specifically oriented towards applications, and it is intended for both pure and applied mathematicians. The reader is required to know classical PDE theory and basic functional analysis.

Download or read book Shape Optimization Problems written by Hideyuki Azegami and published by Springer Nature. This book was released on 2020-09-30 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. In these problems, optimum shapes are obtained from an arbitrary form without any geometrical parameters previously assigned. In particular, problems in which the optimum shape is sought by making a hole in domain are called topology optimization problems. Moreover, a problem in which the optimum shape is obtained based on domain variation is referred to as a shape optimization problem of domain variation type, or a shape optimization problem in a limited sense. Software has been developed to solve these problems, and it is being used to seek practical optimum shapes. However, there are no books explaining such theories beginning with their foundations. The structure of the book is shown in the Preface. The theorems are built up using mathematical results. Therefore, a mathematical style is introduced, consisting of definitions and theorems to summarize the key points. This method of expression is advanced as provable facts are clearly shown. If something to be investigated is contained in the framework of mathematics, setting up a theory using theorems prepared by great mathematicians is thought to be an extremely effective approach. However, mathematics attempts to heighten the level of abstraction in order to understand many things in a unified fashion. This characteristic may baffle readers with an engineering background. Hence in this book, an attempt has been made to provide explanations in engineering terms, with examples from mechanics, after accurately denoting the provable facts using definitions and theorems.

Download or read book Evolutionary and Deterministic Methods for Design Optimization and Control With Applications to Industrial and Societal Problems written by Esther Andrés-Pérez and published by Springer. This book was released on 2018-09-06 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains thirty-five selected papers presented at the International Conference on Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems (EUROGEN 2017). This was one of the Thematic Conferences of the European Community on Computational Methods in Applied Sciences (ECCOMAS). Topics treated in the various chapters reflect the state of the art in theoretical and numerical methods and tools for optimization, and engineering design and societal applications. The volume focuses particularly on intelligent systems for multidisciplinary design optimization (mdo) problems based on multi-hybridized software, adjoint-based and one-shot methods, uncertainty quantification and optimization, multidisciplinary design optimization, applications of game theory to industrial optimization problems, applications in structural and civil engineering optimum design and surrogate models based optimization methods in aerodynamic design.

Download or read book Real time PDE constrained Optimization written by Lorenz T. Biegler and published by SIAM. This book was released on 2007-01-01 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs--and the requirement for rapid solution--pose significant difficulties. A particularly challenging class of PDE-constrained optimization problems is characterized by the need for real-time solution, i.e., in time scales that are sufficiently rapid to support simulation-based decision making. Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. In addition to presenting state-of-the-art algorithms and formulations, the text illustrates these algorithms with a diverse set of applications that includes problems in the areas of aerodynamics, biology, fluid dynamics, medicine, chemical processes, homeland security, and structural dynamics. Audience: readers who have expertise in simulation and are interested in incorporating optimization into their simulations, who have expertise in numerical optimization and are interested in adapting optimization methods to the class of infinite-dimensional simulation problems, or who have worked in "offline" optimization contexts and are interested in moving to "online" optimization.

Download or read book Variational Analysis and Aerospace Engineering written by Giuseppe Buttazzo and published by Springer Science & Business Media. This book was released on 2009-08-21 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Variational Analysis and Aerospace Engineering conference held in Erice, Italy in September 2007 at International School of Mathematics, Guido Stampacchia provided a platform for aerospace engineers and mathematicians to discuss the problems requiring an extensive application of mathematics. This work contains papers presented at the workshop.

Download or read book Large Scale PDE Constrained Optimization written by Lorenz T. Biegler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDE-constrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDE-based optimization. The chapters in this volume collectively assess the state of the art in PDE-constrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research.

Download or read book The NURBS Book written by Les Piegl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until recently B-spline curves and surfaces (NURBS) were principally of interest to the computer aided design community, where they have become the standard for curve and surface description. Today we are seeing expanded use of NURBS in modeling objects for the visual arts, including the film and entertainment industries, art, and sculpture. NURBS are now also being used for modeling scenes for virtual reality applications. These applications are expected to increase. Consequently, it is quite appropriate for The.N'URBS Book to be part of the Monographs in Visual Communication Series. B-spline curves and surfaces have been an enduring element throughout my pro fessional life. The first edition of Mathematical Elements for Computer Graphics, published in 1972, was the first computer aided design/interactive computer graph ics textbook to contain material on B-splines. That material was obtained through the good graces of Bill Gordon and Louie Knapp while they were at Syracuse University. A paper of mine, presented during the Summer of 1977 at a Society of Naval Architects and Marine Engineers meeting on computer aided ship surface design, was arguably the first to examine the use of B-spline curves for ship design. For many, B-splines, rational B-splines, and NURBS have been a bit mysterious.

Download or read book Vehicle Propulsion Systems written by Lino Guzzella and published by Springer Science & Business Media. This book was released on 2007-09-21 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors of this text have written a comprehensive introduction to the modeling and optimization problems encountered when designing new propulsion systems for passenger cars. It is intended for persons interested in the analysis and optimization of vehicle propulsion systems. Its focus is on the control-oriented mathematical description of the physical processes and on the model-based optimization of the system structure and of the supervisory control algorithms.

Download or read book Optimal Shape Design of Aerodynamic Configurations microform a Newton Krylov Approach written by Nemec, Marian and published by National Library of Canada = Bibliothèque nationale du Canada. This book was released on 2003 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: