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Elliptic Problem Solvers

1st Edition - January 28, 1981

Editor: Martin H. Schultz

eBook ISBN:

9 7 8 - 1 - 4 8 3 2 - 5 9 1 2 - 3

Elliptic Problem Solvers provides information pertinent to some aspects of the numerical solution of elliptic partial differential equations. This book presents the advances in… Read more

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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.

Contributors

Preface

Invited 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 Systems

Contributed 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 Simulation

Index