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Numerical Methods For Black Box Software In Computational Continuum Mechanics
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Book Synopsis Numerical Methods for Black-Box Software in Computational Continuum Mechanics by : Sergey I. Martynenko
Download or read book Numerical Methods for Black-Box Software in Computational Continuum Mechanics written by Sergey I. Martynenko and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-11-20 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The organization of the material is presented as follows: This introductory chapter I represents a theoretical analysis of the computational algorithms for a numerical solution of the basic equations in continuum mechanics. In this chapter, the general requirements for computational grids, discretization, and iterative methods for black-box software are examined. Finally, a concept of a two-grid algorithm for (de-)coupled solving multidimensional non-linear (initial-)boundary value problems in continuum mechanics (multiphysics simulation) in complex domains is presented. Chapter II contains descriptions of the sequential Robust Multigrid Technique which is developed as a general-purpose solver in black-box codes. This chapter presents the main components of the Robust Multigrid Technique (RMT) used in the two-grid algorithm (Chapter I) to compute the auxiliary (structured) grid correction. This includes the generation of multigrid structures, computation of index mapping, and integral evaluation. Finite volume discretization on the multigrid structures will be explained by studying a 1D linear model problem. In addition, the algorithmic complexity of RMT and black-box optimization of the problem-dependent components of RMT are analysed. Chapter III provides a description of parallel RMT. This chapter introduces parallel RMT-based algorithms for solving the boundary value problems and initial-boundary value problems in unified manner. Section 1 presents a comparative analysis of the parallel RMT and the sequential V-cycle. Sections 2 and 3 present a geometric and an algebraic parallelism of RMT, i.e. parallelization of the smoothing iterations on the coarse and the levels. A parallel multigrid cycle will be considered in Section 4. A parallel RMT for the time-dependent problems is given in Section 5. Finally, the basic properties of parallel RMT will be summarized in Section 6. Theoretical aspects of the used algorithms for solving multidimensional problems are discussed in Chapters IV. This chapter contains the theoretical aspects of the algorithms used for the numerical solving of the resulting system of linear algebraic equations obtained from discrete multidimensional (initial-)boundary value problems.
Book Synopsis Numerical Methods for Black-Box Software in Computational Continuum Mechanics by : Sergey I. Martynenko
Download or read book Numerical Methods for Black-Box Software in Computational Continuum Mechanics written by Sergey I. Martynenko and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-10-23 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The organization of the material is presented as follows: This introductory chapter I represents a theoretical analysis of the computational algorithms for a numerical solution of the basic equations in continuum mechanics. In this chapter, the general requirements for computational grids, discretization, and iterative methods for black-box software are examined. Finally, a concept of a two-grid algorithm for (de-)coupled solving multidimensional non-linear (initial-)boundary value problems in continuum mechanics (multiphysics simulation) in complex domains is presented. Chapter II contains descriptions of the sequential Robust Multigrid Technique which is developed as a general-purpose solver in black-box codes. This chapter presents the main components of the Robust Multigrid Technique (RMT) used in the two-grid algorithm (Chapter I) to compute the auxiliary (structured) grid correction. This includes the generation of multigrid structures, computation of index mapping, and integral evaluation. Finite volume discretization on the multigrid structures will be explained by studying a 1D linear model problem. In addition, the algorithmic complexity of RMT and black-box optimization of the problem-dependent components of RMT are analysed. Chapter III provides a description of parallel RMT. This chapter introduces parallel RMT-based algorithms for solving the boundary value problems and initial-boundary value problems in unified manner. Section 1 presents a comparative analysis of the parallel RMT and the sequential V-cycle. Sections 2 and 3 present a geometric and an algebraic parallelism of RMT, i.e. parallelization of the smoothing iterations on the coarse and the levels. A parallel multigrid cycle will be considered in Section 4. A parallel RMT for the time-dependent problems is given in Section 5. Finally, the basic properties of parallel RMT will be summarized in Section 6. Theoretical aspects of the used algorithms for solving multidimensional problems are discussed in Chapters IV. This chapter contains the theoretical aspects of the algorithms used for the numerical solving of the resulting system of linear algebraic equations obtained from discrete multidimensional (initial-)boundary value problems.
Book Synopsis Numerical Methods in Computational Mechanics by : Jamshid Ghaboussi
Download or read book Numerical Methods in Computational Mechanics written by Jamshid Ghaboussi and published by CRC Press. This book was released on 2016-11-25 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the numerical algorithms underpinning modern finite element based computational mechanics software. It covers all the major numerical methods that are used in computational mechanics. It reviews the basic concepts in linear algebra and advanced matrix theory, before covering solution of systems of equations, symmetric eigenvalue solution methods, and direct integration of discrete dynamic equations of motion, illustrated with numerical examples. This book suits a graduate course in mechanics based disciplines, and will help software developers in computational mechanics. Increased understanding of the underlying numerical methods will also help practicing engineers to use the computational mechanics software more effectively.
Book Synopsis Mesh Methods for Boundary-Value Problems and Applications by : Ildar B. Badriev
Download or read book Mesh Methods for Boundary-Value Problems and Applications written by Ildar B. Badriev and published by Springer Nature. This book was released on 2022-09-14 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers papers presented at the 13th International Conference on Mesh Methods for Boundary-Value Problems and Applications, which was held in Kazan, Russia, in October 2020. The papers address the following topics: the theory of mesh methods for boundary-value problems in mathematical physics; non-linear mathematical models in mechanics and physics; algorithms for solving variational inequalities; computing science; and educational systems. Given its scope, the book is chiefly intended for students in the fields of mathematical modeling science and engineering. However, it will also benefit scientists and graduate students interested in these fields.
Book Synopsis Numerical Continuum Mechanics by : Vladimir N. Kukudzhanov
Download or read book Numerical Continuum Mechanics written by Vladimir N. Kukudzhanov and published by Walter de Gruyter. This book was released on 2012-12-19 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work focuses on computational methods in continuum thermomechanics. The text is based on the author's lectures, which ensures a didactical and coherent buildup. The main emphasis is put on the presentation of ideas and qualitative considerations, illustrated by specific examples and applications. Conditions and explanations that are essential for the practical application of methods are discussed thoroughly.
Book Synopsis On Some Numerical Methods in Continuum Mechanics by : Paul D. Smith
Download or read book On Some Numerical Methods in Continuum Mechanics written by Paul D. Smith and published by . This book was released on 1971 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings of the GAMM Workshop Discrete Modelling and Discrete Algorithms in Continuum Mechanics by : Thomas Sonar
Download or read book Proceedings of the GAMM Workshop Discrete Modelling and Discrete Algorithms in Continuum Mechanics written by Thomas Sonar and published by Logos Verlag Berlin GmbH. This book was released on 2001 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematics Applied to Continuum Mechanics by : Lee A. Segel
Download or read book Mathematics Applied to Continuum Mechanics written by Lee A. Segel and published by Courier Dover Publications. This book was released on 1987 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern classic analyzes continuum models of fluid flow and solid deformation, examining problems in continuum mechanics, water waves, extremum principles and much more. For upper-level undergraduate and graduate students in the fields of applied mathematics, science and engineering.
Book Synopsis Computational Engineering - Introduction to Numerical Methods by : Michael Schäfer
Download or read book Computational Engineering - Introduction to Numerical Methods written by Michael Schäfer and published by Springer Nature. This book was released on 2021-07-19 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulation methods in all engineering disciplines gains more and more importance. The successful and efficient application of such tools requires certain basic knowledge about the underlying numerical techniques. The text gives a practice-oriented introduction in modern numerical methods as they typically are applied in mechanical, chemical, or civil engineering. Problems from heat transfer, structural mechanics, and fluid mechanics constitute a thematical focus of the text. For the basic understanding of the topic aspects of numerical mathematics, natural sciences, computer science, and the corresponding engineering area are simultaneously important. Usually, the necessary information is distributed in different textbooks from the individual disciplines. In the present text the subject matter is presented in a comprehensive multidisciplinary way, where aspects from the different fields are treated insofar as it is necessary for general understanding. Overarching aspects and important questions related to accuracy, efficiency, and cost effectiveness are discussed. The topics are presented in an introductory manner, such that besides basic mathematical standard knowledge in analysis and linear algebra no further prerequisites are necessary. The book is suitable either for self-study or as an accompanying textbook for corresponding lectures. It can be useful for students of engineering disciplines as well as for computational engineers in industrial practice.
Book Synopsis Computational Continuum Mechanics by : Ahmed A. Shabana
Download or read book Computational Continuum Mechanics written by Ahmed A. Shabana and published by Cambridge University Press. This book was released on 2010-09-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the nonlinear theory of continuum mechanics and demonstrates its use in developing nonlinear computer formulations for large displacement dynamic analysis. Basic concepts used in continuum mechanics are presented and used to develop nonlinear general finite element formulations that can be effectively used in large displacement analysis. The book considers two nonlinear finite element dynamic formulations: a general large deformation finite element formulation and a formulation that can efficiently solve small deformation problems that characterize very stiff structures. The book presents material clearly and systematically, assuming the reader has only basic knowledge in matrix and vector algebra and dynamics. The book is designed for use by advanced undergraduates and first-year graduate students. It is also a reference for researchers, practicing engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dynamics, and other fields of science and engineering using the general continuum mechanics theory.
Book Synopsis Numerical Methods in Contact Mechanics by : Vladislav A. Yastrebov
Download or read book Numerical Methods in Contact Mechanics written by Vladislav A. Yastrebov and published by John Wiley & Sons. This book was released on 2013-02-13 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational contact mechanics is a broad topic which brings together algorithmic, geometrical, optimization and numerical aspects for a robust, fast and accurate treatment of contact problems. This book covers all the basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes for both sequential and parallel computer architectures. The book is self-contained and intended for people working on the implementation and improvement of contact algorithms in a finite element software. Using a new tensor algebra, the authors introduce some original notions in contact kinematics and extend the classical formulation of contact elements. Some classical and new resolution methods for contact problems and associated ready-to-implement expressions are provided. Contents: 1. Introduction to Computational Contact. 2. Geometry in Contact Mechanics. 3. Contact Detection. 4. Formulation of Contact Problems. 5. Numerical Procedures. 6. Numerical Examples. About the Authors Vladislav A. Yastrebov is a postdoctoral-fellow in Computational Solid Mechanics at MINES ParisTech in France. His work in computational contact mechanics was recognized by the CSMA award and by the Prix Paul Caseau of the French Academy of Technology and Electricité de France.
Book Synopsis Cornell University Courses of Study by : Cornell University
Download or read book Cornell University Courses of Study written by Cornell University and published by . This book was released on 2006 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Methods for Structural Mechanics and Dynamics by :
Download or read book Computational Methods for Structural Mechanics and Dynamics written by and published by . This book was released on 1989 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Contact Mechanics by : Peter Wriggers
Download or read book Computational Contact Mechanics written by Peter Wriggers and published by Springer Science & Business Media. This book was released on 2008-04-01 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics of this book span the range from spatial and temporal discretization techniques for contact and impact problems with small and finite deformations over investigations on the reliability of micromechanical contact models over emerging techniques for rolling contact mechanics to homogenization methods and multi-scale approaches in contact problems.
Book Synopsis Computational Methods for Structural Mechanics and Dynamics, Part 1 by :
Download or read book Computational Methods for Structural Mechanics and Dynamics, Part 1 written by and published by . This book was released on 1989 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Solutions to Engineering Problems Using Finite Element Methods by : Vijay Goyal
Download or read book Solutions to Engineering Problems Using Finite Element Methods written by Vijay Goyal and published by . This book was released on 2021-07-31 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on finite element methods, a subset of the field of computational mechanics. Over the past decades, finite element analysis (FEA) has become easier to use and implement, enabling engineering designers to carry out complex and more robust simulations. Furthermore, the steady growth of analysis software coincides with the availability and affordability of high-performance computing architectures, making FEA applications a possible reality for most engineers. Although there are some excellent books for engineering analysis using finite element techniques to solve engineering problems, the intent here is to guide the reader through the finite element method through the very basic concepts to the extent of a first-year graduate student.This book intends to provide the theoretical and practical foundation of the finite element method (FEM). The target audience is first-year graduate students who have had little to no exposure to the subject. However, practicing engineers will also benefit from the approach of this book as they will learn the theoretical aspects of finite element methods, basically, on their own. Thus, we can assure that this book will fill a void in the personal library of many engineers trying or planning to use finite element analysis in their next design. The recommended background to successfully read this book is solid mechanics, calculus, continuum mechanics, theory of elasticity, and basic programming knowledge.When writing this textbook, we have kept the reader in mind at all times. After years of using the earlier versions of the book, engineering graduates from various universities found the approach in this book instrumental in their respective jobs. In teaching and applying the subject for years, we have concluded that students and engineers too often take a "black-box" approach when using FEA software. As a result, they usually lack fundamental knowledge of what the finite element analysis software is doing. Hence, the book's primary goal is to provide a fundamental engineering treatment associated with FEM at a level that is reasonably accessible to those studying the topic for the first time.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1990 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
