An Overlapping Domain Decomposition Preconditioner for a Class of Discontinuous Galerkin Approximations of Advection-diffusion Problems PDF Download

Author: C. Lasser
Publisher:
ISBN:
Category :
Languages : en
Pages : 19

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Author: Tarek Mathew
Publisher: Springer Science & Business Media
ISBN: 354077209X
Category : Mathematics
Languages : en
Pages : 775

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Book Description
Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.

Author: Michel Bercovier
Publisher: Springer Science & Business Media
ISBN: 364202677X
Category : Mathematics
Languages : en
Pages : 384

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Book Description
th This volume contains a selection of 41 refereed papers presented at the 18 International Conference of Domain Decomposition Methods hosted by the School of ComputerScience and Engineering(CSE) of the Hebrew Universityof Jerusalem, Israel, January 12–17, 2008. 1 Background of the Conference Series The International Conference on Domain Decomposition Methods has been held in twelve countries throughout Asia, Europe, the Middle East, and North America, beginning in Paris in 1987. Originally held annually, it is now spaced at roughly 18-month intervals. A complete list of past meetings appears below. The principal technical content of the conference has always been mathematical, but the principal motivation has been to make ef cient use of distributed memory computers for complex applications arising in science and engineering. The leading 15 such computers, at the “petascale” characterized by 10 oating point operations per second of processing power and as many Bytes of application-addressablem- ory, now marshal more than 200,000 independentprocessor cores, and systems with many millions of cores are expected soon. There is essentially no alternative to - main decomposition as a stratagem for parallelization at such scales. Contributions from mathematicians, computerscientists, engineers,and scientists are together n- essary in addressing the challenge of scale, and all are important to this conference.

Author: Andrea Toselli
Publisher: Springer Science & Business Media
ISBN: 3540266623
Category : Mathematics
Languages : en
Pages : 454

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Book Description
This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.

Author: Yunqing Huang
Publisher: Springer Science & Business Media
ISBN: 3642113044
Category : Mathematics
Languages : en
Pages : 484

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Book Description
These are the proceedings of the 19th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linear or nonlinear systems of algebraic equations that arise in various problems in mathematics, computational science, engineering and industry. They are designed for massively parallel computers and take the memory hierarchy of such systems into account. This is essential for approaching peak floating point performance. There is an increasingly well-developed theory which is having a direct impact on the development and improvement of these algorithms.

Author: Alfredo Bermúdez de Castro
Publisher: Springer Science & Business Media
ISBN: 3540342885
Category : Mathematics
Languages : en
Pages : 1202

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These proceedings collect lectures given at ENUMATH 2005, the 6th European Conference on Numerical Mathematics and Advanced Applications held in Santiago de Compostela, Spain in July, 2005. Topics include applications such as fluid dynamics, electromagnetism, structural mechanics, interface problems, waves, finance, heat transfer, unbounded domains, numerical linear algebra, convection-diffusion, as well as methodologies such as a posteriori error estimates, discontinuous Galerkin methods, multiscale methods, optimization, and more.

Author: James Blowey
Publisher: Springer Science & Business Media
ISBN: 3642239145
Category : Mathematics
Languages : en
Pages : 298

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Book Description
This book contains detailed lecture notes on four topics at the forefront of current research in computational mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succint and accurate account of recent research in areas parallel to their own, and graduates in mathematical sciences.

Author: Maxim A. Olshanskii
Publisher: SIAM
ISBN: 1611973457
Category : Mathematics
Languages : en
Pages : 257

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Iterative Methods for Linear Systems offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.

Author: Craig Dwain Collins
Publisher:
ISBN:
Category : Decomposition (Mathematics)
Languages : en
Pages : 198

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Book Description
The application of the techniques of domain decomposition to construct effective preconditioners for systems generated by standard methods such as finite difference or finite element methods has been well-researched in the past few decades. However, results concerning the application of these techniques to systems created by the discontinuous Galerkin method (DG) are much more rare. This dissertation represents the effort to extend the study of two-level nonoverlapping and overlapping additive Schwarz methods for DG discretizations of second- and fourth-order elliptic partial differential equations. In particular, the general Schwarz framework is used to find theoretical bounds for the condition numbers of the preconditioned systems corresponding to both the nonoverlapping and overlapping additive Schwarz methods. In addition, the impact on the performance of the preconditioners caused by varying the penalty parameters inherent to DG methods is investigated. Another topic of investigation is the choice of course subspace made for the two-level Schwarz methods. The results of in-depth computational experiments performed to validate and study various aspects of the theory are presented. In addition, the design and implementation of the methods are discussed.

Author:
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 920

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