Elliptic Problem Solvers

Author : Martin H. Schultz
Publisher : Academic Press
ISBN 13 : 1483259129
Total Pages : 459 pages
Book Rating : 4.23/5 ( download)

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Download or read book Elliptic Problem Solvers written by Martin H. Schultz and published by Academic Press. This book was released on 2014-05-10 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Garrett Birkhoff
Publisher : Academic Press
ISBN 13 : 1483263398
Total Pages : 588 pages
Book Rating : 4.97/5 ( download)

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Download or read book Elliptic Problem Solvers written by Garrett Birkhoff and published by Academic Press. This book was released on 2014-05-10 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Per-Gunnar Martinsson
Publisher : SIAM
ISBN 13 : 1611976049
Total Pages : 332 pages
Book Rating : 4.45/5 ( download)

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Download or read book Fast Direct Solvers for Elliptic PDEs written by Per-Gunnar Martinsson and published by SIAM. This book was released on 2019-12-16 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.

Author : Garrett Birkhoff
Publisher :
ISBN 13 :
Total Pages : 600 pages
Book Rating : 4.81/5 ( download)

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Download or read book Elliptic Problem Solvers II written by Garrett Birkhoff and published by . This book was released on 1984 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.79/5 ( download)

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Download or read book Elliptic Problem Solvers written by and published by . This book was released on 1984 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Marián Vajtersic
Publisher : Springer Science & Business Media
ISBN 13 : 9401707014
Total Pages : 310 pages
Book Rating : 4.15/5 ( download)

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Download or read book Algorithms for Elliptic Problems written by Marián Vajtersic and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : John R. Rice
Publisher : Springer Science & Business Media
ISBN 13 : 1461250188
Total Pages : 491 pages
Book Rating : 4.80/5 ( download)

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Download or read book Solving Elliptic Problems Using ELLPACK written by John R. Rice and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: ELLP ACK is a many faceted system for solving elliptic partial differential equations. It is a forerunner of the very high level, problem solving environments or expert systems that will become common in the next decade. While it is still far removed from the goals of the future, it is also far advanced compared to the Fortran library approach in common current use. Many people will find ELLP ACK an easy way to solve simple or moderately complex elliptic problems. Others will be able to solve really hard problems by digging a little deeper into ELLP ACK. ELLP ACK is a research tool for the study of numerical methods for solving elliptic problems. Its original purpose was for the evaluation and comparison of numerical software for elliptic problems. Simple examples of this use are given in Chapters 9-11. The general conclusion is that there are many ways to solve most elliptic problems, there are large differences in their efficiency and the most common ways are often less efficient, sometimes dramatically so.

Author : Martin H. Schultz
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.23/5 ( download)

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Download or read book Elliptic Problem Solvers written by Martin H. Schultz and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Eugene G. D'yakonov
Publisher : CRC Press
ISBN 13 : 135108366X
Total Pages : 590 pages
Book Rating : 4.69/5 ( download)

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Download or read book Optimization in Solving Elliptic Problems written by Eugene G. D'yakonov and published by CRC Press. This book was released on 2018-05-04 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Craig C. Douglas
Publisher : SIAM
ISBN 13 : 9780898718171
Total Pages : 153 pages
Book Rating : 4.71/5 ( download)

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Download or read book A Tutorial on Elliptic PDE Solvers and Their Parallelization written by Craig C. Douglas and published by SIAM. This book was released on 2003-01-01 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This compact yet thorough tutorial is the perfect introduction to the basic concepts of solving partial differential equations (PDEs) using parallel numerical methods. In just eight short chapters, the authors provide readers with enough basic knowledge of PDEs, discretization methods, solution techniques, parallel computers, parallel programming, and the run-time behavior of parallel algorithms to allow them to understand, develop, and implement parallel PDE solvers. Examples throughout the book are intentionally kept simple so that the parallelization strategies are not dominated by technical details.