Efficient Preconditioned Solution Methods For Elliptic Partial Differential Equations
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Efficient Preconditioned Solution Methods For Elliptic Partial Differential Equations
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Author : Owe Axelsson
language : en
Publisher: Bentham Science Publishers
Release Date : 2011
Efficient Preconditioned Solution Methods For Elliptic Partial Differential Equations written by Owe Axelsson and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This e-book presents several research areas of elliptical problems solved by differential equations. The mathematical models explained in this e-book have been contributed by experts in the field and can be applied to a wide range of real life examples. M
A Survey Of Preconditioned Iterative Methods
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Author : Are Magnus Bruaset
language : en
Publisher: Routledge
Release Date : 2018-12-13
A Survey Of Preconditioned Iterative Methods written by Are Magnus Bruaset and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-13 with Mathematics categories.
The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are w
Spectral Methods For Uncertainty Quantification
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Author : Olivier Le Maitre
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-11
Spectral Methods For Uncertainty Quantification written by Olivier Le Maitre and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-11 with Science categories.
This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.
Computational Techniques And Applications Proceedings Of The Sixth Biennial Conference
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Author : Henry J Gardner
language : en
Publisher: World Scientific
Release Date : 1994-06-28
Computational Techniques And Applications Proceedings Of The Sixth Biennial Conference written by Henry J Gardner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-06-28 with Mathematics categories.
This volume contains papers on computational mathematics, development, implementation, and application of numerical algorithms, the development and application of computational systems, and numerical modelling. Also featured are reports on applications of advanced computer architectures and innovative visualisation techniques. It will be a help for developers and implementors of computational methods who wish to find out more about the work of those applying the technology to problems in engineering and science, and vice versa.
Iciam 87
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Author : James McKenna
language : en
Publisher: SIAM
Release Date : 1988-01-01
Iciam 87 written by James McKenna and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
Petsc For Partial Differential Equations Numerical Solutions In C And Python
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Author : Ed Bueler
language : en
Publisher: SIAM
Release Date : 2020-10-22
Petsc For Partial Differential Equations Numerical Solutions In C And Python written by Ed Bueler and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-22 with Mathematics categories.
The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.
Numerical Methods And Applications 1994
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Author : Guri I Marchuk
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Numerical Methods And Applications 1994 written by Guri I Marchuk and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
This book presents new original numerical methods that have been developed to the stage of concrete algorithms and successfully applied to practical problems in mathematical physics. The book discusses new methods for solving stiff systems of ordinary differential equations, stiff elliptic problems encountered in problems of composite material mechanics, Navier-Stokes systems, and nonstationary problems with discontinuous data. These methods allow natural paralleling of algorithms and will find many applications in vector and parallel computers.
Optimal Control Of Partial Differential Equations
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Author : Andrea Manzoni
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
Optimal Control Of Partial Differential Equations written by Andrea Manzoni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.
Proceedings Of The 19th International Meshing Roundtable
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Author : Suzanne Shontz
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-30
Proceedings Of The 19th International Meshing Roundtable written by Suzanne Shontz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-30 with Computers categories.
The papers in this volume were selected for presentation at the 19th International Meshing Roundtable (IMR), held October 3–6, 2010 in Chattanooga, Tennessee, USA. The conference was started by Sandia National Laboratories in 1992 as a small meeting of organizations striving to establish a common focus for research and development in the field of mesh generation. Now after 19 consecutive years, the International Meshing Roundtable has become recognized as an international focal point annually attended by researchers and developers from dozens of co- tries around the world. The 19th International Meshing Roundtable consists of technical presentations from contributed papers, research notes, keynote and invited talks, short course presentations, and a poster session and competition. The Program Committee would like to express its appreciation to all who participate to make the IMR a successful and enriching experience. The papers in these proceedings were selected by the Program Committee from among numerous submissions. Based on input from peer reviews, the committee selected these papers for their perceived quality, originality, and appropriateness to the theme of the International Meshing Roundtable. We would like to thank all who submitted papers. We would also like to thank the colleagues who provided reviews of the submitted papers. The names of the reviewers are acknowledged in the following pages. We extend special thanks to Jacqueline Hunter for her time and effort to make the 19th IMR another outstanding conference.
Numerical Mathematics And Advanced Applications Enumath 2017
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Author : Florin Adrian Radu
language : en
Publisher: Springer
Release Date : 2019-01-05
Numerical Mathematics And Advanced Applications Enumath 2017 written by Florin Adrian Radu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-05 with Mathematics categories.
This book collects many of the presented papers, as plenary presentations, mini-symposia invited presentations, or contributed talks, from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) 2017. The conference was organized by the University of Bergen, Norway from September 25 to 29, 2017. Leading experts in the field presented the latest results and ideas in the designing, implementation, and analysis of numerical algorithms as well as their applications to relevant, societal problems. ENUMATH is a series of conferences held every two years to provide a forum for discussing basic aspects and new trends in numerical mathematics and scientific and industrial applications. These discussions are upheld at the highest level of international expertise. The first ENUMATH conference was held in Paris in 1995 with successive conferences being held at various locations across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), and Ankara (2015).