Elliptic Problem Solvers
Published on 10. May 2014
458 pages
978-1-4832-5912-3 (ISBN)
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.
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Martin Schultz
Elliptic Problem Solvers: v.1
Book
01/1981
Academic Press
€61.39
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Content
ContributorsPrefaceInvited Papers A Multi-Level Iterative Method for Nonlinear Elliptic Equations Solving Elliptic Problems: 1930-1980 Multigrid Solvers on Parallel Computers Implementing Techniques for Elliptic Problems on Vector Processors On Some Trends in Elliptic Problem Solvers Co-Energy Methods for Elliptic Flow and Related Problems ELLPACK: Progress and Plans The ITPACK Package for Large Sparse Linear SystemsContributed Papers Efficient Fortran Subprograms for the Solution of Elliptic Partial Differential Equations Iterative Methods for Finite Element Equations Predictor-Corrector Methods for the Solution of Time-Dependent Parabolic Problems on Parallel Processors Efficient Solution of the Biharmonic Equation Attainable Accuracy of Compact Discretizations of the Poisson Equation The Concept of Rigidity and Its Implementation Theorems of Stein-Rosenberg Type II. Optimal Paths of Relaxation in the Complex Plane Sparse Vectorized Direct Solution of Elliptic Problems Multi-Grid and ICCG for Problems with Interfaces An Ad Hoc Sor Method On Preconditioned Iterative Methods for Elliptic Partial Differential Equations Block Relaxation Strategies On the Numerical Solution of Nonlinear Elliptic PDEs Arising from Semiconductor Device Modeling Non-Standard Multigrid Techniques Using Checkered Relaxation and Intermediate Grids Some Experiments in Solving Stiff Oscillatory Ordinary Differential Equations A Numerical Method for Solving Elliptic Boundary Value Problems in Unbounded Domains Applications of Transfinite ("Blending-Function") Interpolation to the Approximate Solution of Elliptic Problems Application of Parallel Processor to the Solution of Finite Difference Problems Vector Algorithms for Elliptic Partial Differential Equations Based on the Jacobi Method Adapting Iterative Algorithms Developed for Symmetric Systems to Nonsymmetric Systems Comparison of Methods of Solution of the Finite Element Equations for the Large Displacement Analysis of Arches Mesh Generation by Conformai and Quasiconformal Mappings Block Iterative Methods A Mesh-Parameter-Continuation Method Capacitance Matrix Methods-A Brief Survey Gem Solutions of Elliptic and Mixed Problems with Non-Separable 5- and 9-Point Operators A Parallel Block Stiefel Method for Solving Positive Definite Systems Numerical Solution of Coupled Systems of Partial Differential Equations in One Spatial Variable Time On the Choice of Discretization for Solving PDEs on a Multi-Processor A Software Package for Elliptic Partial Differential Equations An Empirical Investigation of Methods for Nonsymmetric Linear Systems Semiconductor Device SimulationIndex
