Elliptic Problem Solvers
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Elliptic Problem Solvers
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Author : Martin H. Schultz
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Elliptic Problem Solvers written by Martin H. Schultz and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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
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Author : Garrett Birkhoff
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Elliptic Problem Solvers written by Garrett Birkhoff and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.
Discontinuous Galerkin Methods For Solving Elliptic And Parabolic Equations
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Author : Beatrice Riviere
language : en
Publisher: SIAM
Release Date : 2008-12-18
Discontinuous Galerkin Methods For Solving Elliptic And Parabolic Equations written by Beatrice Riviere and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-18 with Mathematics categories.
Focuses on three primal DG methods, covering both theory and computation, and providing the basic tools for analysis.
Algorithms For Elliptic Problems
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Author : Marián Vajtersic
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Algorithms For Elliptic Problems written by Marián Vajtersic 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 2013-03-09 with Computers categories.
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.
Elliptic Problem Solvers Conference
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Author :
language : en
Publisher:
Release Date : 1981
Elliptic Problem Solvers Conference written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
The Finite Element Method For Elliptic Problems
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Author : P.G. Ciarlet
language : en
Publisher: Elsevier
Release Date : 1978-01-01
The Finite Element Method For Elliptic Problems written by P.G. Ciarlet and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978-01-01 with Mathematics categories.
The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author's experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on "Additional Bibliography and Comments should provide many suggestions for conducting seminars.
On Some Trends In Elliptic Problem Solvers
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Author : S. C. Eisenstat
language : en
Publisher:
Release Date : 1981
On Some Trends In Elliptic Problem Solvers written by S. C. Eisenstat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Elliptic boundary value problems are at the core of many systems of partial differential equations occurring in mechanics. Examples of applications include fluid dynamics, semiconductor device modelling, and structural analysis. Thus, it is important to have efficient and robust elliptic problem solvers. In this paper we discuss some of the issues involved in the design of a high-technology elliptic problem solver. In particular, we will concentrate our attention on the design of a modular, heterogeneous multi-processor elliptic problem solver consisting of a host computer and one or more peripheral processors.
Fast Direct Solvers For Elliptic Pdes
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Author : Per-Gunnar Martinsson
language : en
Publisher: SIAM
Release Date : 2019-12-16
Fast Direct Solvers For Elliptic Pdes written by Per-Gunnar Martinsson and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-16 with Mathematics categories.
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.
Elliptic Problem Solvers
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Author :
language : en
Publisher:
Release Date : 1984
Elliptic Problem Solvers written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with 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.