Numerical Methods For Black Box Software In Computational Continuum Mechanics

Author : Sergey I. Martynenko
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311131975X
Total Pages : 194 pages
Book Rating : 4.59/5 ( download)

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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.

Author : Sergey I. Martynenko
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111319563
Total Pages : 148 pages
Book Rating : 4.68/5 ( download)

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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.

Author : Ildar B. Badriev
Publisher : Springer Nature
ISBN 13 : 3030878090
Total Pages : 607 pages
Book Rating : 4.92/5 ( download)

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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.

Author : Matteo Cicuttin
Publisher : Springer Nature
ISBN 13 : 3030814777
Total Pages : 138 pages
Book Rating : 4.79/5 ( download)

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Download or read book Hybrid High-Order Methods written by Matteo Cicuttin and published by Springer Nature. This book was released on 2021-11-11 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive coverage of hybrid high-order methods for computational mechanics. The first three chapters offer a gentle introduction to the method and its mathematical foundations for the diffusion problem. The next four chapters address applications of increasing complexity in the field of computational mechanics: linear elasticity, hyperelasticity, wave propagation, contact, friction, and plasticity. The last chapter provides an overview of the main implementation aspects including some examples of Matlab code. The book is primarily intended for graduate students, researchers, and engineers working in related fields of application, and it can also be used as a support for graduate and doctoral lectures.

Author : Bilen Emek Abali
Publisher : Springer
ISBN 13 : 9811024448
Total Pages : 308 pages
Book Rating : 4.43/5 ( download)

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Download or read book Computational Reality written by Bilen Emek Abali and published by Springer. This book was released on 2016-10-22 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of continuum mechanics for mechanical, thermodynamical, and electrodynamical systems. It shows how to obtain governing equations and it applies them by computing the reality. It uses only open-source codes developed under the FEniCS project and includes codes for 20 engineering applications from mechanics, fluid dynamics, applied thermodynamics, and electromagnetism. Moreover, it derives and utilizes the constitutive equations including coupling terms, which allow to compute multiphysics problems by incorporating interactions between primitive variables, namely, motion, temperature, and electromagnetic fields. An engineering system is described by the primitive variables satisfying field equations that are partial differential equations in space and time. The field equations are mostly coupled and nonlinear, in other words, difficult to solve. In order to solve the coupled, nonlinear system of partial differential equations, the book uses a novel collection of open-source packages developed under the FEniCS project. All primitive variables are solved at once in a fully coupled fashion by using finite difference method in time and finite element method in space.

Author : Michael Schäfer
Publisher : Springer Nature
ISBN 13 : 3030760278
Total Pages : 374 pages
Book Rating : 4.74/5 ( download)

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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.

Author : Vladislav A. Yastrebov
Publisher : John Wiley & Sons
ISBN 13 : 1118648056
Total Pages : 303 pages
Book Rating : 4.56/5 ( download)

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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.

Author : Wolfgang Gentzsch
Publisher :
ISBN 13 : 9780990400035
Total Pages : 246 pages
Book Rating : 4.34/5 ( download)

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Download or read book Vectorization of Computer Programs with Applications to Computational Fluid Dynamics written by Wolfgang Gentzsch and published by . This book was released on 1984 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Cornell University
Publisher :
ISBN 13 :
Total Pages : 712 pages
Book Rating : 4.29/5 ( download)

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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:

Author : Vijay Goyal
Publisher :
ISBN 13 : 9780578254869
Total Pages : pages
Book Rating : 4.67/5 ( download)

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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.