Download or read book Sensitivity Analysis of Differential Algebraic Equations and Partial Differential Equations written by Y. Cao and published by . This book was released on 2005 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 differential-algebraic equation (DAE) and time-dependent partial differential equation (PDE) systems.

Download or read book Design Sensitivity Analysis written by Lisa G. Stanley and published by SIAM. This book was released on 2002-01-01 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an understandable introduction to one approach to design sensitivity computation and illustrates some of the important mathematical and computational issues inherent in using the sensitivity equation method (SEM) for partial differential equations. The authors use basic models to illustrate the computational issues that one might encounter when applying the SEM in a laboratory or research setting, while providing an overview of applications and computational issues regarding sensitivity calculations performed by way of continuous sensitivity equation methods (CSEM).

Download or read book Sensitivity Analysis and Computation for Partial Differential Equations written by Lisa Gale Davis and published by . This book was released on 2008 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of practical numerical methods for simulation of partial differential equations leads to problems of convergence, accuracy and efficiency. Verification of a computational algorithm consists in part of establishing a convergence theory for the discretized equations. It is well known that the long time behavior of a system may not be captured even by "convergent" approximating methods and additional requirements must be placed on the scheme to ensure the discretized equations capture the correct asymptotic behavior. Even on finite intervals, there are always uncertainties in the problem data that can be a source of difficulty for accurate simulation of nonlinear problems. These uncertainties lead to uncertainty in the computed results and should be considered as part of the verification step. This research gives preliminary results showing how sensitivity analysis can be used to provide a practical precursor to dynamic transitions and quantify numerical uncertainty in simulations of nonlinear parabolic partial differential equations.

Download or read book Adjoint Sensitivity Analysis for Optimal Control of Non Smooth Differential Algebraic Equations written by Ralf Hannemann-Tamás and published by . This book was released on 2013-01-28 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Gesetz betreffend die Erstattung von Rechtsanwaltsgeb hren in Armensachen und nderung des Gerichtskostengesetzes written by and published by . This book was released on 1928 with total page 2 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Sensitivity Analysis of Initial Value Problems with Mixed Ode s and Algebraic Equations written by M. Caracotsios and published by . This book was released on 1984 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: An efficient method is described for sensitivity analysis of nonlinear initial value problems, which may include algebraic equations as well as ordinary differential equations. The linearity of the sensitivity equations is utilized to solve them directly via the local Jacobian of the state equations. The method is implemented with the implicit integrator DASSL and is demonstrated on a stiff industrial reaction model. Keywords: Numerical integration, Stiff equations, Parametric sensitivities, Initial value problems, Newtons method, Chemical kinetics.

Download or read book Model Parametric Sensitivity Analysis and Nonlinear Parameter Estimation written by Malamas Caracotsios and published by . This book was released on 1986 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Solution of Initial Value Problems in Differential Algebraic Equations written by K. E. Brenan and published by SIAM. This book was released on 1996-01-01 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes some of the places where differential-algebraic equations (DAE's) occur.

Download or read book Introduction to Shape Optimization written by Jan Sokolowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is motivated largely by a desire to solve shape optimization prob lems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems. Many such problems can be formulated as the minimization of functionals defined over a class of admissible domains. Shape optimization is quite indispensable in the design and construction of industrial structures. For example, aircraft and spacecraft have to satisfy, at the same time, very strict criteria on mechanical performance while weighing as little as possible. The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. g. such as the weight of the structure) and yet simultaneously satisfies specific constraints (like thickness, strain energy, or displacement bounds). The geometry of the structure can be considered as a given domain in the three-dimensional Euclidean space. The domain is an open, bounded set whose topology is given, e. g. it may be simply or doubly connected. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed. In general the cost functional takes the form of an integral over the domain or its boundary where the integrand depends smoothly on the solution of a boundary value problem.

Download or read book Surveys in Differential Algebraic Equations IV written by Achim Ilchmann and published by Springer. This book was released on 2017-03-08 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs) which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - History of DAEs - DAE aspects of mechanical multibody systems - Model reduction of DAEs - Observability for DAEs - Numerical Analysis for DAEs The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

Download or read book A Sensitivity Analysis of Ordinary Differential Equations written by Setareh Oveisi and published by . This book was released on 2005 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Sensitivity Uncertainty Analysis Volume 1 written by Dan G. Cacuci and published by CRC Press. This book was released on 2003-05-28 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: As computer-assisted modeling and analysis of physical processes have continued to grow and diversify, sensitivity and uncertainty analyses have become indispensable investigative scientific tools in their own right. While most techniques used for these analyses are well documented, there has yet to appear a systematic treatment of the method based on adjoint operators, which is applicable to a much wider variety of problems than methods traditionally used in control theory. This book fills that gap, focusing on the mathematical underpinnings of the Adjoint Sensitivity Analysis Procedure (ASAP) and the use of deterministically obtained sensitivities for subsequent uncertainty analysis.

Download or read book Sensitivity Analysis of Linearly implicit Differential algebraic Systems by One step Extrapolation written by and published by . This book was released on 2002 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "In this work we present an approach for the sensitivity analysis of linearly-implicit differential-algebraic equation systems. Solutions for both, states and sensitivities are obtained by applying an extrapolated linearly implicit Euler discretization scheme. This approach is compared to the widely used sensitivity extensions of multi-step BDF methods by means of case studies. Especially, we point out the benefit of this method in the context of dynamic optimization using the sequential approach."

Download or read book Topics in Modal Analysis Volume 10 written by Michael Mains and published by Springer. This book was released on 2015-04-15 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Modal Analysis, Volume 10: Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015, the tenth volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Experimental Techniques Processing Modal Data Rotating Machinery Acoustics Adaptive Structures Biodynamics Damping

Download or read book Design and Sensitivity Analysis of Inverse Problems Governed by Partial Differential Equations written by Isaac Paul Sunseri and published by . This book was released on 2022 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Simulation and Modelling of Electronic and Biochemical Systems written by Jaijeet Roychowdhury and published by Now Publishers Inc. This book was released on 2009 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulation and modelling have been growing in importance and seeing steadily increasing practical application. The proliferation of applications and physical domains for which simulation technologies are now needed, compounded by generally increased complexity, has expanded the scope of numerical simulation and modelling within CAD and spurred new research directions. Numerical Simulation and Modelling of Electronic and Biochemical Systems provides an introduction to the fundamentals of numerical simulation, and to the basics of modelling electronic circuits and biochemical reactions. The emphasis is on capturing a minimal set of important concepts succinctly, but concretely enough that the reader will be left with an adequate foundation for further independent exploration. Starting from mathematical models of basic electronic elements, circuits are modelled as nonlinear differential-algebraic equation (DAE) systems. Two basic techniques - quiescent steady state and transient - for solving these differential equations systems are then developed. It is then shown how biochemical reactions can also be modelled deterministically as DAEs. Following this, frequency domain techniques for finding sinusoidal steady states of linear DAEs are developed, as are direct and adjoint techniques for computing parameter sensitivities and the effects of stationary random noise. For readers interested in a glimpse of topics beyond these basics, an introduction to nonlinear periodic steady state methods (harmonic balance and shooting) and the multitime partial differential equation formulation is provided. Also provided is an overview of model order reduction, an important topic of current research that has roots in numerical simulation algorithms. Finally, sample applications of nonlinear oscillator macromodels - in circuits (PLLs), biochemical reaction-diffusion systems and nanoelectronics - are presented.