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Numerical Solution of Elliptic Differential Equations by Reduction to the Interface

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 773/5 ( reviews)

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Book Synopsis Numerical Solution of Elliptic Differential Equations by Reduction to the Interface by : Boris N. Khoromskij

Download or read book Numerical Solution of Elliptic Differential Equations by Reduction to the Interface written by Boris N. Khoromskij. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: During the last decade essential progress has been achieved in the analysis and implementation of multilevel/rnultigrid and domain decomposition methods to explore a variety of real world applications. An important trend in mod ern numerical simulations is the quick improvement of computer technology that leads to the well known paradigm (see, e. g. , [78,179]): high-performance computers make it indispensable to use numerical methods of almost linear complexity in the problem size N, to maintain an adequate scaling between the computing time and improved computer facilities as N increases. In the h-version of the finite element method (FEM), the multigrid iteration real izes an O(N) solver for elliptic differential equations in a domain n c IRd d with N = O(h- ) , where h is the mesh parameter. In the boundary ele ment method (BEM) , the traditional panel clustering, fast multi-pole and wavelet based methods as well as the modern hierarchical matrix techniques are known to provide the data-sparse approximations to the arising fully populated stiffness matrices with almost linear cost O(Nr log?Nr), where 1 d Nr = O(h - ) is the number of degrees of freedom associated with the boundary. The aim of this book is to introduce a wider audience to the use of a new class of efficient numerical methods of almost linear complexity for solving elliptic partial differential equations (PDEs) based on their reduction to the interface.

Parallel Computational Fluid Dynamics 2007

2009-04-21 Mathematics
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Release : 2009-04-21
Genre : Mathematics
Kind : eBook
Book Rating : 441/5 ( reviews)

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Book Synopsis Parallel Computational Fluid Dynamics 2007 by : Ismail H. Tuncer

Download or read book Parallel Computational Fluid Dynamics 2007 written by Ismail H. Tuncer. This book was released on 2009-04-21. Available in PDF, EPUB and Kindle. Book excerpt: At the 19th Annual Conference on Parallel Computational Fluid Dynamics held in Antalya, Turkey, in May 2007, the most recent developments and implementations of large-scale and grid computing were presented. This book, comprised of the invited and selected papers of this conference, details those advances, which are of particular interest to CFD and CFD-related communities. It also offers the results related to applications of various scientific and engineering problems involving flows and flow-related topics. Intended for CFD researchers and graduate students, this book is a state-of-the-art presentation of the relevant methodology and implementation techniques of large-scale computing.

Recent Advances in Algorithmic Differentiation

2012-07-30 Mathematics
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Release : 2012-07-30
Genre : Mathematics
Kind : eBook
Book Rating : 235/5 ( reviews)

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Book Synopsis Recent Advances in Algorithmic Differentiation by : Shaun Forth

Download or read book Recent Advances in Algorithmic Differentiation written by Shaun Forth. This book was released on 2012-07-30. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings represent the state of knowledge in the area of algorithmic differentiation (AD). The 31 contributed papers presented at the AD2012 conference cover the application of AD to many areas in science and engineering as well as aspects of AD theory and its implementation in tools. For all papers the referees, selected from the program committee and the greater community, as well as the editors have emphasized accessibility of the presented ideas also to non-AD experts. In the AD tools arena new implementations are introduced covering, for example, Java and graphical modeling environments or join the set of existing tools for Fortran. New developments in AD algorithms target the efficiency of matrix-operation derivatives, detection and exploitation of sparsity, partial separability, the treatment of nonsmooth functions, and other high-level mathematical aspects of the numerical computations to be differentiated. Applications stem from the Earth sciences, nuclear engineering, fluid dynamics, and chemistry, to name just a few. In many cases the applications in a given area of science or engineering share characteristics that require specific approaches to enable AD capabilities or provide an opportunity for efficiency gains in the derivative computation. The description of these characteristics and of the techniques for successfully using AD should make the proceedings a valuable source of information for users of AD tools.

BAIL 2008 - Boundary and Interior Layers

2009-06-10 Mathematics
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Release : 2009-06-10
Genre : Mathematics
Kind : eBook
Book Rating : 051/5 ( reviews)

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Book Synopsis BAIL 2008 - Boundary and Interior Layers by : Alan Hegarty

Download or read book BAIL 2008 - Boundary and Interior Layers written by Alan Hegarty. This book was released on 2009-06-10. Available in PDF, EPUB and Kindle. Book excerpt: These Proceedings contain a selection of the lectures given at the conference BAIL 2008: Boundary and Interior Layers – Computational and Asymptotic Methods, which was held from 28th July to 1st August 2008 at the University of Limerick, Ireland. The ?rst three BAIL conferences (1980, 1982, 1984) were organised by Professor John Miller in Trinity College Dublin, Ireland. The next seven were held in Novosibirsk (1986), Shanghai (1988), Colorado (1992), Beijing (1994), Perth (2002),Toulouse(2004),and Got ̈ tingen(2006).With BAIL 2008the series returned to Ireland. BAIL 2010 is planned for Zaragoza. The BAIL conferences strive to bring together mathematicians and engineers whose research involves layer phenomena,as these two groups often pursue largely independent paths. BAIL 2008, at which both communities were well represented, succeeded in this regard. The lectures given were evenly divided between app- cations and theory, exposing all conference participants to a broad spectrum of research into problems exhibiting solutions with layers. The Proceedings give a good overview of current research into the theory, app- cation and solution (by both numerical and asymptotic methods) of problems that involve boundaryand interior layers. In addition to invited and contributed lectures, the conference included four mini-symposia devoted to stabilized ?nite element methods, asymptotic scaling of wall-bounded ?ows, systems of singularly p- turbed differential equations, and problems with industrial applications (supported by MACSI, the Mathematics Applications Consortium for Science and Industry). These titles exemplify the mix of interests among the participants.

Sparse Grids and Applications

2012-10-13 Mathematics
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Release : 2012-10-13
Genre : Mathematics
Kind : eBook
Book Rating : 030/5 ( reviews)

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Book Synopsis Sparse Grids and Applications by : Jochen Garcke

Download or read book Sparse Grids and Applications written by Jochen Garcke. This book was released on 2012-10-13. Available in PDF, EPUB and Kindle. Book excerpt: In the recent decade, there has been a growing interest in the numerical treatment of high-dimensional problems. It is well known that classical numerical discretization schemes fail in more than three or four dimensions due to the curse of dimensionality. The technique of sparse grids helps overcome this problem to some extent under suitable regularity assumptions. This discretization approach is obtained from a multi-scale basis by a tensor product construction and subsequent truncation of the resulting multiresolution series expansion. This volume of LNCSE is a collection of the papers from the proceedings of the workshop on sparse grids and its applications held in Bonn in May 2011. The selected articles present recent advances in the mathematical understanding and analysis of sparse grid discretization. Aspects arising from applications are given particular attention.

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