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Elliptic Problem Solvers

Elliptic Problem Solvers PDF Author: Martin H. Schultz
Publisher: Academic Press
ISBN: 1483259129
Category : Mathematics
Languages : en
Pages : 459

Book Description
Elliptic Problem Solvers provides information pertinent to some aspects of the numerical solution of elliptic partial differential equations. This book presents the advances in developing elliptic problem solvers and analyzes their performance. Organized into 40 chapters, this book begins with an overview of the approximate solution of using a standard Galerkin method employing piecewise linear triangular finite elements. This text then defines the types of vector architecture and discusses the variation in performance that can occur on a vector processor as a function of algorithm and implementation. Other chapters consider the implementation of techniques for elliptical problems. This book discusses as well the six techniques for the solution of nonsymmetric linear systems arising from finite difference discretization of the convection-diffusion equation. The final chapter deals with the basic semiconductor device equations. This book is a valuable resource for electrical and computer engineers, scientists, computer programmers, pure mathematicians, and research workers.

Elliptic Problem Solvers

Elliptic Problem Solvers PDF Author: Martin H. Schultz
Publisher: Academic Press
ISBN: 1483259129
Category : Mathematics
Languages : en
Pages : 459

Book Description
Elliptic Problem Solvers provides information pertinent to some aspects of the numerical solution of elliptic partial differential equations. This book presents the advances in developing elliptic problem solvers and analyzes their performance. Organized into 40 chapters, this book begins with an overview of the approximate solution of using a standard Galerkin method employing piecewise linear triangular finite elements. This text then defines the types of vector architecture and discusses the variation in performance that can occur on a vector processor as a function of algorithm and implementation. Other chapters consider the implementation of techniques for elliptical problems. This book discusses as well the six techniques for the solution of nonsymmetric linear systems arising from finite difference discretization of the convection-diffusion equation. The final chapter deals with the basic semiconductor device equations. This book is a valuable resource for electrical and computer engineers, scientists, computer programmers, pure mathematicians, and research workers.

Elliptic Problem Solvers

Elliptic Problem Solvers PDF Author: Garrett Birkhoff
Publisher: Academic Press
ISBN: 1483263398
Category : Mathematics
Languages : en
Pages : 588

Book Description
Elliptic Problem Solvers, II covers the proceedings of the Elliptic Problem Solvers Conference, held at the Naval Postgraduate School in Monterey, California from January 10 to 12, 1983. The book focuses on various aspects of the numerical solution of elliptic boundary value problems. The selection first offers information on building elliptic problem solvers with ELLPACK; presentation and evolution of the club module; and a fourth order accurate fast direct method for the Helmholtz equation. The text then examines the ITPACK project, CMMPAK, solving elliptic problems on an array processor system, and parallel architectures for iterative methods on adaptive, block structured grids. Topics include adaptive solution algorithm, data structure, elliptic problem solvers, input data, and vector ITPACK. The publication ponders on conjugate gradient preconditioners for vector and parallel processors; an algebra for systolic computation; and an incomplete-Cholesky factorization by a matrix partition algorithm. The book also tackles the numerical solution of a model equation near the onset of the Rayleigh-Benard instability; numerical methods for solving coupled semiconductor equations on a minicomputer; and analysis of nonlinear elliptic systems arising in reaction/diffusion modeling. The selection is highly recommended for researchers interested in elliptic problem solvers.

Selected Papers from the Second Conference on Parallel Processing for Scientific Computing

Selected Papers from the Second Conference on Parallel Processing for Scientific Computing PDF Author: Charles William Gear
Publisher: SIAM
ISBN: 9780898712162
Category : Computers
Languages : en
Pages : 296

Book Description
Proceedings -- Parallel Computing.

Scientific and Technical Aerospace Reports

Scientific and Technical Aerospace Reports PDF Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 702

Book Description


Technical Abstract Bulletin

Technical Abstract Bulletin PDF Author:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 220

Book Description


Algorithms for Elliptic Problems

Algorithms for Elliptic Problems PDF Author: Marián Vajtersic
Publisher: Springer Science & Business Media
ISBN: 9401707014
Category : Computers
Languages : en
Pages : 310

Book Description
This volume deals with problems of modern effective algorithms for the numerical solution of the most frequently occurring elliptic partial differential equations. From the point of view of implementation, attention is paid to algorithms for both classical sequential and parallel computer systems. The first two chapters are devoted to fast algorithms for solving the Poisson and biharmonic equation. In the third chapter, parallel algorithms for model parallel computer systems of the SIMD and MIMD types are described. The implementation aspects of parallel algorithms for solving model elliptic boundary value problems are outlined for systems with matrix, pipeline and multiprocessor parallel computer architectures. A modern and popular multigrid computational principle which offers a good opportunity for a parallel realization is described in the next chapter. More parallel variants based in this idea are presented, whereby methods and assignments strategies for hypercube systems are treated in more detail. The last chapter presents VLSI designs for solving special tridiagonal linear systems of equations arising from finite-difference approximations of elliptic problems. For researchers interested in the development and application of fast algorithms for solving elliptic partial differential equations using advanced computer systems.

Current Trends in Scientific Computing

Current Trends in Scientific Computing PDF Author: Zhangxin Chen
Publisher: American Mathematical Soc.
ISBN: 0821832611
Category : Mathematics
Languages : en
Pages : 386

Book Description
This volume contains 36 research papers written by prominent researchers. The papers are based on a large satellite conference on scientific computing held at the International Congress of Mathematics (ICM) in Xi'an, China. Topics covered include a variety of subjects in modern scientific computing and its applications, such as numerical discretization methods, linear solvers, parallel computing, high performance computing, and applications to solid and fluid mechanics, energy, environment, and semiconductors. The book will serve as an excellent reference work for graduate students and researchers working with scientific computing for problems in science and engineering.

Government Reports Announcements & Index

Government Reports Announcements & Index PDF Author:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 530

Book Description


Recent Trends in Numerical Analysis

Recent Trends in Numerical Analysis PDF Author: D. Trigiante
Publisher: Nova Publishers
ISBN: 9781560728856
Category : Mathematics
Languages : en
Pages : 364

Book Description
The contributions for this volume, dedicated to honour the 65th birthday of Professor I Galligani, have been numerous and cover a wide range of topics of the current Numerical Analysis and of its applications.

Optimization in Solving Elliptic Problems

Optimization in Solving Elliptic Problems PDF Author: Eugene G. D'yakonov
Publisher: CRC Press
ISBN: 135108366X
Category : Mathematics
Languages : en
Pages : 590

Book Description
Optimization in Solving Elliptic Problems focuses on one of the most interesting and challenging problems of computational mathematics - the optimization of numerical algorithms for solving elliptic problems. It presents detailed discussions of how asymptotically optimal algorithms may be applied to elliptic problems to obtain numerical solutions meeting certain specified requirements. Beginning with an outline of the fundamental principles of numerical methods, this book describes how to construct special modifications of classical finite element methods such that for the arising grid systems, asymptotically optimal iterative methods can be applied. Optimization in Solving Elliptic Problems describes the construction of computational algorithms resulting in the required accuracy of a solution and having a pre-determined computational complexity. Construction of asymptotically optimal algorithms is demonstrated for multi-dimensional elliptic boundary value problems under general conditions. In addition, algorithms are developed for eigenvalue problems and Navier-Stokes problems. The development of these algorithms is based on detailed discussions of topics that include accuracy estimates of projective and difference methods, topologically equivalent grids and triangulations, general theorems on convergence of iterative methods, mixed finite element methods for Stokes-type problems, methods of solving fourth-order problems, and methods for solving classical elasticity problems. Furthermore, the text provides methods for managing basic iterative methods such as domain decomposition and multigrid methods. These methods, clearly developed and explained in the text, may be used to develop algorithms for solving applied elliptic problems. The mathematics necessary to understand the development of such algorithms is provided in the introductory material within the text, and common specifications of algorithms that have been developed for typical problems in mathema