Download or read book Advances in Numerical Analysis Large scale matrix problems and the numerical solution of partial differential equations written by William Allan Light and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Large scale Matrix Problems and the Numerical Solution of Partial Differential Equations written by John Gilbert and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing contributions from the 5th SERC Summer School in Numerical Analysis, held at Lancaster University in 1992, this volume covers a wide range of research developments in numerical analysis.
Download or read book Large scale Matrix Problems and the Numerical Solution of Partial Differential Equations written by John E. Gilbert and published by . This book was released on 1994 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces advanced students and professionals to cutting-edge research in numerical analysis. Featuring a collection of contributors renowned for their expertise in the subject, the book focuses in particular on the use of parallel computers, both for solving large sets of linear equations and for calculating the eigensystems of large matrices. Issues related to the solution of such equations--such as the preconditioning of elliptic problems, the study of semi-conductors, methods for the solution of hydrodynamic problems--are discussed in detail. Written at a level both accessible to graduate students and stimulating for established researchers, this book will be welcomed by a wide range of people studying numerical analysis.
Download or read book Hierarchical Matrices Algorithms and Analysis written by Wolfgang Hackbusch and published by Springer. This book was released on 2015-12-21 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.
Download or read book Recent Advances in Numerical Analysis written by Carl De Boor and published by Academic Press. This book was released on 2014-05-10 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Advances in Numerical Analysis provides information pertinent to the developments in numerical analysis. This book covers a variety of topics, including positive functions, Sobolev spaces, computing paths, partial differential equations, and perturbation theory. Organized into 12 chapters, this book begins with an overview of stability conditions for numerical methods that can be expressed in the form that some associated function is positive. This text then examines the polynomial approximation theory having applications to finite element Galerkin methods. Other chapters consider the numerical condition of polynomials by examining three particular problem areas, namely, the representation of polynomials, algebraic equations, and the problem of orthogonalization. This book discusses as well a general theory that leads to a systematic way to prepare the initial data. The final chapter deals with the derivation of the Kronecker canonical form. This book is a valuable resource for applied mathematicians, numerical analysts, physicists, engineers, and research workers.
Download or read book Numerical Analysis and Its Applications written by Svetozar D. Margenov and published by Springer. This book was released on 2009-02-07 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 4th International Conference on Numerical Analysis and Its Applications, NAA 2008, held in Lozenetz, Bulgaria in June 2008. The 61 revised full papers presented together with 13 invited papers were carefully selected during two rounds of reviewing and improvement. The papers address all current aspects of numerical analysis and discuss a wide range of problems concerning recent achievements in physics, chemistry, engineering, and economics. A special focus is given to numerical approximation and computational geometry, numerical linear algebra and numerical solution of transcendental equations, numerical methods for differential equations, numerical modeling, and high performance scientific computing.
Download or read book Approximation of Large Scale Dynamical Systems written by Athanasios C. Antoulas and published by SIAM. This book was released on 2009-06-25 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are used to simulate, and sometimes control, the behavior of physical and artificial processes such as the weather and very large-scale integration (VLSI) circuits. The increasing need for accuracy has led to the development of highly complex models. However, in the presence of limited computational accuracy and storage capabilities model reduction (system approximation) is often necessary. Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations. It addresses the issue of model reduction and the resulting trade-offs between accuracy and complexity. Special attention is given to numerical aspects, simulation questions, and practical applications.
Download or read book Large Scale Scientific Computing written by Deuflhard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the new and rapidly expanding field of scientific computing is understood in a double sense: as computing for scientific and engineering problems and as the science of doing such computations. Thus scientific computing touches at one side mathematical modelling (in the various fields of applications) and at the other side computer science. As soon as the mathematical models de scribe the features of real life processes in sufficient detail, the associated computations tend to be large scale. As a consequence, interest more and more focusses on such numerical methods that can be expected to cope with large scale computational problems. Moreover, given the algorithms which are known to be efficient on a tradi tional computer, the question of implementation on modern supercomputers may get crucial. The present book is the proceedings of a meeting on "Large Scale Scientific Computing" , that was held a t the Oberwolfach Mathematical Institute (July 14-19, 1985) under the auspices of the Sonderforschungsbereich 123 of the University of Heidelberg. Participants included applied scientists with computational interests, numerical analysts, and experts on modern parallel computers. 'l'he purpose of the meeting was to establish a common under standing of recent issues in scientific computing, especially in view of large scale problems. Fields of applications, which have been covered, included semi-conductor design, chemical combustion, flow through porous media, climatology, seismology, fluid dynami. cs, tomography, rheology, hydro power plant optimization, subwil. y control, space technology.
Download or read book Numerical Analysis A R Mitchell 75th Birthday Volume written by D F Griffiths and published by World Scientific. This book was released on 1996-05-15 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is intended to mark the 75th birthday of A R Mitchell, of the University of Dundee. It consists of a collection of articles written by numerical analysts having links with Ron Mitchell, as colleagues, collaborators, former students, or as visitors to Dundee. Ron Mitchell is known for his books and articles contributing to the numerical analysis of partial differential equations; he has also made major contributions to the development of numerical analysis in the UK and abroad, and his many human qualitites are such that he is held in high regard and looked on with great affection by the numerical analysis community. The list of contributors is evidence of the esteem in which he is held, and of the way in which his influence has spread through his former students and fellow workers. In addition to contributions relevant to his own specialist subjects, there are also papers on a wide range of subjects in numerical analysis.
Download or read book Matrix Based Multigrid written by Yair Shapira and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many important problems in applied science and engineering, such as the Navier Stokes equations in fluid dynamics, the primitive equations in global climate mod eling, the strain-stress equations in mechanics, the neutron diffusion equations in nuclear engineering, and MRIICT medical simulations, involve complicated sys tems of nonlinear partial differential equations. When discretized, such problems produce extremely large, nonlinear systems of equations, whose numerical solution is prohibitively costly in terms of time and storage. High-performance (parallel) computers and efficient (parallelizable) algorithms are clearly necessary. Three classical approaches to the solution of such systems are: Newton's method, Preconditioned Conjugate Gradients (and related Krylov-space acceleration tech niques), and multigrid methods. The first two approaches require the solution of large sparse linear systems at every iteration, which are themselves often solved by multigrid methods. Developing robust and efficient multigrid algorithms is thus of great importance. The original multigrid algorithm was developed for the Poisson equation in a square, discretized by finite differences on a uniform grid. For this model problem, multigrid exhibits extremely rapid convergence, and actually solves the problem in the minimal possible time. The original algorithm uses rediscretization of the partial differential equation (POE) on each grid in the hierarchy of coarse grids that are used. However, this approach would not work for more complicated problems, such as problems on complicated domains and nonuniform grids, problems with variable coefficients, and non symmetric and indefinite equations. In these cases, matrix-based multi grid methods are in order.
Download or read book Control Perspectives on Numerical Algorithms and Matrix Problems written by Amit Bhaya and published by SIAM. This book was released on 2006-03-01 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book organizes the analysis and design of iterative numerical methods from a control perspective. A variety of applications are discussed, including iterative methods for linear and nonlinear systems of equations, neural networks for linear and quadratic programming problems and integration and shooting methods for ordinary differential equations.
Download or read book Numerical Solution of Partial Differential Equations written by J.G. Gram and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the transcripts of the invited lectures presented at the NATO Advanced Study Institute on "Numerical Solution of Partial Differential Equations". The Study Institute was held at the Netherlands-Norwegian Reactor School, Institutt for Atomenergi, Kjeller, Norway, 20th - 24th August 1973. The members of the Scientific Advisory Committee were: A. R. Mitchell, University of Dundee, Scotland I. HoI and, University of Trondheim, Norway T. Havie, UniverSity of Trondheim, Norway The members of the Organizing Committee were: E. Andersen, Institutt for Atomenergi, Kjeller, Norway G. E. Fladmark, Institutt for Atomenergi, Kjeller, Norway J. G. Gram, Institutt for Atomenergi, Kjeller, Norway The aim of the Study Institute was to bring together mathe maticians and engineers working with numerical methods. The papers presented covered both theory and application of methods for solution of partial differential equations. The topics were finite element methods, finite difference methods, and methods for solution of linear and nonlinear systems of equations with application to continuum mechanics and heat transfer. The total number of participants was 68. Their names are given at the end of the book. The publication of these proceed ings could be realized through the kind cooperation of the lec turers. The Advanced Study Institute was financially sponsored by NATO Scientific Affairs Division. The Organizing Committee wishes to express its gratitude for this support. Valuable assistance was given by Mrs. G.
Download or read book PETSc for Partial Differential Equations Numerical Solutions in C and Python written by Ed Bueler and published by SIAM. This book was released on 2020-10-22 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Efficient Numerical Methods for Non local Operators written by Steffen Börm and published by European Mathematical Society. This book was released on 2010 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hierarchical matrices present an efficient way of treating dense matrices that arise in the context of integral equations, elliptic partial differential equations, and control theory. While a dense $n\times n$ matrix in standard representation requires $n^2$ units of storage, a hierarchical matrix can approximate the matrix in a compact representation requiring only $O(n k \log n)$ units of storage, where $k$ is a parameter controlling the accuracy. Hierarchical matrices have been successfully applied to approximate matrices arising in the context of boundary integral methods, to construct preconditioners for partial differential equations, to evaluate matrix functions, and to solve matrix equations used in control theory. $\mathcal{H}^2$-matrices offer a refinement of hierarchical matrices: Using a multilevel representation of submatrices, the efficiency can be significantly improved, particularly for large problems. This book gives an introduction to the basic concepts and presents a general framework that can be used to analyze the complexity and accuracy of $\mathcal{H}^2$-matrix techniques. Starting from basic ideas of numerical linear algebra and numerical analysis, the theory is developed in a straightforward and systematic way, accessible to advanced students and researchers in numerical mathematics and scientific computing. Special techniques are required only in isolated sections, e.g., for certain classes of model problems.
Download or read book Numerical Methods for Solving Partial Differential Equations written by George F. Pinder and published by John Wiley & Sons. This book was released on 2018-02-05 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to numerical methods for simulating physical-chemical systems This book offers a systematic, highly accessible presentation of numerical methods used to simulate the behavior of physical-chemical systems. Unlike most books on the subject, it focuses on methodology rather than specific applications. Written for students and professionals across an array of scientific and engineering disciplines and with varying levels of experience with applied mathematics, it provides comprehensive descriptions of numerical methods without requiring an advanced mathematical background. Based on its author’s more than forty years of experience teaching numerical methods to engineering students, Numerical Methods for Solving Partial Differential Equations presents the fundamentals of all of the commonly used numerical methods for solving differential equations at a level appropriate for advanced undergraduates and first-year graduate students in science and engineering. Throughout, elementary examples show how numerical methods are used to solve generic versions of equations that arise in many scientific and engineering disciplines. In writing it, the author took pains to ensure that no assumptions were made about the background discipline of the reader. Covers the spectrum of numerical methods that are used to simulate the behavior of physical-chemical systems that occur in science and engineering Written by a professor of engineering with more than forty years of experience teaching numerical methods to engineers Requires only elementary knowledge of differential equations and matrix algebra to master the material Designed to teach students to understand, appreciate and apply the basic mathematics and equations on which Mathcad and similar commercial software packages are based Comprehensive yet accessible to readers with limited mathematical knowledge, Numerical Methods for Solving Partial Differential Equations is an excellent text for advanced undergraduates and first-year graduate students in the sciences and engineering. It is also a valuable working reference for professionals in engineering, physics, chemistry, computer science, and applied mathematics.
Download or read book Topics in Numerical Analysis II written by John J.H. Miller and published by Elsevier. This book was released on 2012-12-02 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Numerical Analysis II contains in complete form, the papers given by the invited speakers to the Conference on Numerical Analysis held under the auspices of the National Committee for Mathematics of the Royal Irish Academy at University College, Dublin from 29th July to 2nd August, 1974. In addition, the titles of the contributed papers are listed together with the names and addresses of the authors who presented them at the conference. This book is divided into 20 chapters that present the papers in their entirety. They discuss such topics as applications of approximation theory to numerical analysis; interior regularity and local convergence of Galerkin finite element approximations for elliptic equations; and numerical estimates for the error of Gauss-Jacobi quadrature formulae. Some remarks on the unified treatment of elementary functions by microprogramming; application of finite difference methods to exploration seismology; and variable coefficient multistep methods for ordinary differential equations applied to parabolic partial differential equations are also presented. Other chapters cover realistic estimates for generic constants in multivariate pointwise approximation; matching of essential boundary conditions in the finite element method; and collocation, difference equations, and stitched function representations. This book will be of interest to practitioners in the fields of mathematics and computer science.
Download or read book Large Scale Scientific Computation written by Seymour V. Parter and published by Elsevier. This book was released on 2014-05-10 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large Scale Scientific Computation is a collection of papers that deals with specialized architectural considerations, efficient use of existing computers, software developments, large scale projects in diverse disciplines, and mathematical approaches to basic algorithmic problems. One paper describes numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques applied in many institutions such as in Laboratoire Central des Ponts et Chaussees, Avions Marcel Dassault et Breguet Aviation. Another paper discusses computer-structured design techniques to improve the reliability, efficiency, and accuracy of future production codes. Computer modelling is a potent tool in numerical weather prediction relying on observation, analysis, initialization, and model development. One paper illustrates a systolic algorithm for matrix triangulation, as well as its uses in the Cholesky decomposition of covariance matrices. Another paper describes the Transient Reactor Analysis Code (TRAC) designed to deal with internal flow problems of nuclear reactors. One paper explains the application of large-scale aerodynamic simulation where the programmer can use finite difference techniques in which a large number of mesh points are strategically and orderly placed in the domain of the flow field. The collection is intended for undergraduates in mathematics, programming, computer science, or engineering courses, and designers or researchers involved in industrial facilities, aeronautics, and nuclear design.
