Author : Owe Axelsson
Publisher : Bentham Science Publishers
Page : 153 pages
File Size : 47,22 MB
Release : 2011
Category : Mathematics
ISBN : 1608052915
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
Author : Owe Axelsson
Publisher :
Page : 156 pages
File Size : 19,39 MB
Release : 2011-10-05
Category : Differential equations, Elliptic
ISBN : 9781608056101
This book presents several research areas of elliptical problems solved by differential equations. The mathematical models explained in this book have been contributed by experts in the field and can be applied to a wide range of real life examples. Methods explained include pre-conditioned conjugate grid models, higher order discretization and finite element mesh generation. This book should be a useful reference for scholars and professionals interested in elliptical partial differential equations.
Author : Josef Malek
Publisher : SIAM
Page : 106 pages
File Size : 31,80 MB
Release : 2014-12-22
Category : Mathematics
ISBN : 161197383X
Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs?is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during formulation of the mathematical model through to efficient numerical solution of the algebraic problem. The book?s central concept, preconditioning of the conjugate gradient method, is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system. In this text, however, preconditioning is connected to the PDE analysis, and the infinite-dimensional formulation of the conjugate gradient method and its discretization and preconditioning are linked together. This text challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.?
Author : Olivier Le Maitre
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 44,85 MB
Release : 2010-03-11
Category : Science
ISBN : 9048135206
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.
Author : Tarek Mathew
Publisher : Springer Science & Business Media
Page : 775 pages
File Size : 37,29 MB
Release : 2008-06-25
Category : Mathematics
ISBN : 354077209X
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 : Florin Adrian Radu
Publisher : Springer
Page : 993 pages
File Size : 45,10 MB
Release : 2019-01-05
Category : Computers
ISBN : 3319964151
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).
Author : James McKenna
Publisher : SIAM
Page : 412 pages
File Size : 34,56 MB
Release : 1988-01-01
Category : Mathematics
ISBN : 9780898712247
Author : Are Magnus Bruaset
Publisher : Routledge
Page : 180 pages
File Size : 13,31 MB
Release : 2018-12-13
Category : Mathematics
ISBN : 1351469363
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
Author : Ed Bueler
Publisher : SIAM
Page : 407 pages
File Size : 25,94 MB
Release : 2020-10-22
Category : Mathematics
ISBN : 1611976316
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.
Author :
Publisher : Academic Press
Page : 399 pages
File Size : 41,94 MB
Release : 1991-12-11
Category : Computers
ISBN : 0080577482
Advances in Electronics and Electron Physics
