Dirichlet Dirichlet Domain Decomposition Methods For Elliptic Problems H And Hp Finite Element Discretizations

Author : Korneev Vadim Glebiovich,Langer Ulrich
Publisher : World Scientific
Page : 484 pages
File Size : 53,9 Mb
Release : 2015-01-29
Category : Mathematics
ISBN : 9789814578479

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Dirichlet-dirichlet Domain Decomposition Methods For Elliptic Problems: H And Hp Finite Element Discretizations by Korneev Vadim Glebiovich,Langer Ulrich Pdf

Domain decomposition (DD) methods provide powerful tools for constructing parallel numerical solution algorithms for large scale systems of algebraic equations arising from the discretization of partial differential equations. These methods are well-established and belong to a fast developing area. In this volume, the reader will find a brief historical overview, the basic results of the general theory of domain and space decomposition methods as well as the description and analysis of practical DD algorithms for parallel computing. It is typical to find in this volume that most of the presented DD solvers belong to the family of fast algorithms, where each component is efficient with respect to the arithmetical work. Readers will discover new analysis results for both the well-known basic DD solvers and some DD methods recently devised by the authors, e.g., for elliptic problems with varying chaotically piecewise constant orthotropism without restrictions on the finite aspect ratios.The hp finite element discretizations, in particular, by spectral elements of elliptic equations are given significant attention in current research and applications. This volume is the first to feature all components of Dirichlet-Dirichlet-type DD solvers for hp discretizations devised as numerical procedures which result in DD solvers that are almost optimal with respect to the computational work. The most important DD solvers are presented in the matrix/vector form algorithms that are convenient for practical use.

Author : Vadim Glebovich Korneev,Ulrich Langer
Publisher : World Scientific Publishing Company
Page : 492 pages
File Size : 51,8 Mb
Release : 2014-12-31
Category : Decomposition (Mathematics).
ISBN : UCSD:31822038943213

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Dirichlet-Dirichlet Domain Decomposition Methods for Elliptic Problems by Vadim Glebovich Korneev,Ulrich Langer Pdf

Domain decomposition (DD) methods provide powerful tools for constructing parallel numerical solution algorithms for large scale systems of algebraic equations arising from the discretization of partial differential equations. These methods are well-established and belong to a fast developing area. In this volume, the reader will find a brief historical overview, the basic results of the general theory of domain and space decomposition methods as well as the description and analysis of practical DD algorithms for parallel computing. It is typical to find in this volume that most of the presented DD solvers belong to the family of fast algorithms, where each component is efficient with respect to the arithmetical work. Readers will discover new analysis results for both the well-known basic DD solvers and some DD methods recently devised by the authors, e.g., for elliptic problems with varying chaotically piecewise constant orthotropism without restrictions on the finite aspect ratios.The hp finite element discretizations, in particular, by spectral elements of elliptic equations are given significant attention in current research and applications. This volume is the first to feature all components of Dirichlet-Dirichlet-type DD solvers for hp discretizations devised as numerical procedures which result in DD solvers that are almost optimal with respect to the computational work. The most important DD solvers are presented in the matrix/vector form algorithms that are convenient for practical use.

Author : Thomas Apel,Olaf Steinbach
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 41,8 Mb
Release : 2012-07-16
Category : Technology & Engineering
ISBN : 9783642303166

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Advanced Finite Element Methods and Applications by Thomas Apel,Olaf Steinbach Pdf

This volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines the numerical analysis of finite element algorithms, their efficient implementation on state of the art hardware architectures, and the collaboration with engineers and practitioners. In this spirit, this volume contains contributions of former students and collaborators indicating the broad range of their interests in the theory and application of finite element methods. Topics cover the analysis of domain decomposition and multilevel methods, including hp finite elements, hybrid discontinuous Galerkin methods, and the coupling of finite and boundary element methods; the efficient solution of eigenvalue problems related to partial differential equations with applications in electrical engineering and optics; and the solution of direct and inverse field problems in solid mechanics.

Author : Ildar B. Badriev,Victor Banderov,Sergey A. Lapin
Publisher : Springer Nature
Page : 607 pages
File Size : 40,6 Mb
Release : 2022-09-14
Category : Mathematics
ISBN : 9783030878092

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Mesh Methods for Boundary-Value Problems and Applications by Ildar B. Badriev,Victor Banderov,Sergey A. Lapin Pdf

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 : Manfred Kaltenbacher
Publisher : Springer
Page : 251 pages
File Size : 50,8 Mb
Release : 2017-07-10
Category : Technology & Engineering
ISBN : 9783319590387

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Computational Acoustics by Manfred Kaltenbacher Pdf

The book presents a state-of-art overview of numerical schemes efficiently solving the acoustic conservation equations (unknowns are acoustic pressure and particle velocity) and the acoustic wave equation (pressure of acoustic potential formulation). Thereby, the different equations model both vibrational- and flow-induced sound generation and its propagation. Latest numerical schemes as higher order finite elements, non-conforming grid techniques, discontinuous Galerkin approaches and boundary element methods are discussed. Main applications will be towards aerospace, rail and automotive industry as well as medical engineering. The team of authors are able to address these topics from the engineering as well as numerical points of view.

Author : Thomas Apel,Ulrich Langer,Arnd Meyer,Olaf Steinbach
Publisher : Springer
Page : 428 pages
File Size : 47,5 Mb
Release : 2019-06-28
Category : Mathematics
ISBN : 9783030142445

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Advanced Finite Element Methods with Applications by Thomas Apel,Ulrich Langer,Arnd Meyer,Olaf Steinbach Pdf

Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.

Author : Jan Mandel,Charbel Farhat,Xiao-Chuan Cai
Publisher : American Mathematical Soc.
Page : 554 pages
File Size : 41,7 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821809884

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Domain Decomposition Methods 10 by Jan Mandel,Charbel Farhat,Xiao-Chuan Cai Pdf

This volume contains the proceedings of the Tenth International Conference on Domain Decomposition Methods, which focused on the latest developments in realistic applications in structural mechanics, structural dynamics, computational fluid dynamics, and heat transfer. The proceedings of these conferences have become standard references in the field and contain seminal papers as well as the latest theoretical results and reports on practical applications.This volume is divided into four parts: the first part contains invited papers (some of which survey developments over the past decade), and the other parts gather material from minisymposia and contributed presentations under three headings: Algorithms, Theory, and Applications. The electronic version is available at no additional charge to purchasers of the print volume. Access instructions are provided in the book. There is also the option to purchase only the electronic version.

Author : Alfio Quarteroni
Publisher : American Mathematical Soc.
Page : 484 pages
File Size : 41,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851586

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Domain Decomposition Methods in Science and Engineering by Alfio Quarteroni Pdf

This book contains the proceedings of the Sixth International Conference on Domain Decomposition, held in June 1992 in Como, Italy. Developments in this area are driven by advances in computer technology as well as by a strengthening in the mathematical foundations of the subject. Compared to just a few years ago, experts have much more experience with difficult applications and have accumulated solid evidence that these methods provide valuable tools for solving problems in science and engineering. Much of the work in this field focuses on developing numerical methods for large algebraic systems, methods central to producing efficient codes for computational fluid dynamics, elasticity, and other core problems of continuum mechanics. These methods hold the promise of allowing simulations of very high resolution with relative ease. This approach allows for the flexibility of using different numerical methods and different models, each appropriate for the subregion at hand, to solve large problems in a cost-effective way. Containing contributions by international experts in this area, this book reports on the state-of-the-art in the growing field of domain decomposition.

Author : Zbigniew Leyk
Publisher : Unknown
Page : 38 pages
File Size : 51,6 Mb
Release : 1990
Category : Electronic
ISBN : CORNELL:31924059480107

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Domain Decomposition Methods for Nonselfadjoint Operators by Zbigniew Leyk Pdf

Author : Barbara I. Wohlmuth
Publisher : Springer Science & Business Media
Page : 199 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642567674

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Discretization Methods and Iterative Solvers Based on Domain Decomposition by Barbara I. Wohlmuth Pdf

Domain decomposition methods provide powerful and flexible tools for the numerical approximation of partial differential equations arising in the modeling of many interesting applications in science and engineering. This book deals with discretization techniques on non-matching triangulations and iterative solvers with particular emphasis on mortar finite elements, Schwarz methods and multigrid techniques. New results on non-standard situations as mortar methods based on dual basis functions and vector field discretizations are analyzed and illustrated by numerical results. The role of trace theorems, harmonic extensions, dual norms and weak interface conditions is emphasized. Although the original idea was used successfully more than a hundred years ago, these methods are relatively new for the numerical approximation. The possibilites of high performance computations and the interest in large- scale problems have led to an increased research activity.

Author : Ulrich Langer,Marco Discacciati,David E. Keyes,Olof Widlund,Walter Zulehner
Publisher : Springer Science & Business Media
Page : 656 pages
File Size : 53,5 Mb
Release : 2008-01-02
Category : Mathematics
ISBN : 9783540751991

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Domain Decomposition Methods in Science and Engineering XVII by Ulrich Langer,Marco Discacciati,David E. Keyes,Olof Widlund,Walter Zulehner Pdf

Domain decomposition is an active, interdisciplinary research field concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models. This volume contains selected papers presented at the 17th International Conference on Domain Decomposition Methods in Science and Engineering. It presents the newest domain decomposition techniques and examines their use in the modeling and simulation of complex problems.

Author : Pavel Solin,Karel Segeth,Ivo Dolezel
Publisher : CRC Press
Page : 404 pages
File Size : 40,7 Mb
Release : 2003-07-28
Category : Mathematics
ISBN : 9780203488041

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Higher-Order Finite Element Methods by Pavel Solin,Karel Segeth,Ivo Dolezel Pdf

The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and

Author : R. Glowinski
Publisher : Society for Industrial and Applied Mathematics (SIAM)
Page : 462 pages
File Size : 43,7 Mb
Release : 1988
Category : Mathematics
ISBN : UOM:39015015705216

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First International Symposium on Domain Decomposition Methods for Partial Differential Equations by R. Glowinski Pdf

Author : Anonim
Publisher : Unknown
Page : 672 pages
File Size : 48,7 Mb
Release : 2003
Category : Engineering mathematics
ISBN : CORNELL:31924089800050

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Computational Methods in Applied Mathematics by Anonim Pdf

Author : James H. Bramble,Joseph E. Pasciak,Alfred H. Schatz
Publisher : Unknown
Page : 62 pages
File Size : 55,9 Mb
Release : 1987
Category : Electronic
ISBN : CORNELL:31924074851985

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The Construction of Preconditioners for Elliptic Problems by Substructuring, IV by James H. Bramble,Joseph E. Pasciak,Alfred H. Schatz Pdf