Stochastic Finite Elements

Stochastic Finite Elements
Title Stochastic Finite Elements PDF eBook
Author Roger G. Ghanem
Publisher Courier Corporation
Pages 260
Release 2003-01-01
Genre Technology & Engineering
ISBN 9780486428185

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This text analyzes a class of discrete mathematical models of engineering systems, identifying key issues and reviewing relevant theoretical concepts, with particular attention to a spectral approach. 1991 edition.

Stochastic Finite Elements: A Spectral Approach

Stochastic Finite Elements: A Spectral Approach
Title Stochastic Finite Elements: A Spectral Approach PDF eBook
Author Roger G. Ghanem
Publisher Springer Science & Business Media
Pages 217
Release 2012-12-06
Genre Science
ISBN 1461230942

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This monograph considers engineering systems with random parame ters. Its context, format, and timing are correlated with the intention of accelerating the evolution of the challenging field of Stochastic Finite Elements. The random system parameters are modeled as second order stochastic processes defined by their mean and covari ance functions. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used' to represent these processes in terms of a countable set of un correlated random vari ables. Thus, the problem is cast in a finite dimensional setting. Then, various spectral approximations for the stochastic response of the system are obtained based on different criteria. Implementing the concept of Generalized Inverse as defined by the Neumann Ex pansion, leads to an explicit expression for the response process as a multivariate polynomial functional of a set of un correlated random variables. Alternatively, the solution process is treated as an element in the Hilbert space of random functions, in which a spectral repre sentation in terms of the Polynomial Chaoses is identified. In this context, the solution process is approximated by its projection onto a finite subspace spanned by these polynomials.

Stochastic Finite Elements

Stochastic Finite Elements
Title Stochastic Finite Elements PDF eBook
Author Roger Ghanem
Publisher Springer Verlag
Pages 214
Release 1991
Genre Technology & Engineering
ISBN 9780387974569

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A comprehensive treatment of the theories and concepts behind analyzing a class of discrete mathematical models of engineering systems whose properties and excitations can be represented as random processes. The spectral approach extends the deterministic finite element method to the space of random functions. Addressed to students and researchers in mechanical and other branches of engineering. Annotation copyrighted by Book News, Inc., Portland, OR

Spectral and High Order Methods for Partial Differential Equations

Spectral and High Order Methods for Partial Differential Equations
Title Spectral and High Order Methods for Partial Differential Equations PDF eBook
Author Jan S. Hesthaven
Publisher Springer Science & Business Media
Pages 507
Release 2010-10-29
Genre Mathematics
ISBN 3642153372

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The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.

The Stochastic Finite Element Method

The Stochastic Finite Element Method
Title The Stochastic Finite Element Method PDF eBook
Author Michael Kleiber
Publisher Wiley
Pages 336
Release 1993-02-02
Genre Technology & Engineering
ISBN 9780471936268

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Combines two crucial techniques created to deal with complex problems of modern engineering--the finite element method and stochastic analysis. By utilizing the computationally effective finite element approach, it offers a means to obtain extremely useful insight into the way in which ever-existing structural uncertainties propagate. Includes the latest research on the topic of stochastic finite elements. Computer programs, available on request, demonstrate the theory.

Automated Solution of Differential Equations by the Finite Element Method

Automated Solution of Differential Equations by the Finite Element Method
Title Automated Solution of Differential Equations by the Finite Element Method PDF eBook
Author Anders Logg
Publisher Springer Science & Business Media
Pages 723
Release 2012-02-24
Genre Computers
ISBN 3642230997

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This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Introduction to Matrix Analytic Methods in Stochastic Modeling

Introduction to Matrix Analytic Methods in Stochastic Modeling
Title Introduction to Matrix Analytic Methods in Stochastic Modeling PDF eBook
Author G. Latouche
Publisher SIAM
Pages 331
Release 1999-01-01
Genre Mathematics
ISBN 0898714257

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Presents the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner.