Elliptic Problem Solvers

Martin H. Schultz

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9780126326208
• eBook ISBN: 9781483259123
• Topic: Mathematics
• Subtopic: Calculus
• Index: Mathematics

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.

Table of contents

• Front Cover
• Elliptic Problem Solvers
• Copyright Page
• Table of Contents
• Contributors
• Preface
• CHAPTER 1. A MULTI-LEVEL ITERATIVE METHOD FOR NONLINEAR ELLIPTIC EQUATIONS
• CHAPTER 2. SOLVING ELLIPTIC PROBLEMS: 1930-1980
• CHAPTER 3. MULTIGRID SOLVERS ON PARALLEL COMPUTERS
• CHAPTER 4. IMPLEMENTING TECHNIQUES FOR ELLIPTIC PROBLEMS ON VECTOR PROCESSORS
• CHAPTER 5. ON SOME TRENDS IN ELLIPTIC PROBLEM SOLVERS
• CHAPTER 6. CO-ENERGY METHODS FOR ELLIPTIC FLOW AND RELATED PROBLEMS
• CHAPTER 7. ELLPACK: PROGRESS AND PLANS
• CHAPTER 8. THE ITPACK PACKAGE FOR LARGE SPARSE LINEAR SYSTEMS
• CHAPTER 9. EFFICIENT FORTRAN SUBPROGRAMS FOR THE SOLUTION OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS
• CHAPTER 10. ITERATIVE METHODS FOR FINITE ELEMENT EQUATIONS
• CHAPTER 11. PREDICTOR-CORRECTOR METHODS FOR THE SOLUTION OF TIME-DEPENDENT PARABOLIC PROBLEMS ON PARALLEL PROCESSORS
• CHAPTER 12. EFFICIENT SOLUTION OF THE BIHARMONIC EQUATION
• CHAPTER 13. ATTAINABLE ACCURACY OF COMPACT DISCRETIZATIONS OF THE POISSON EQUATION
• CHAPTER 14. THE CONCEPT OF RIGIDITY AND ITS IMPLEMENTATION
• CHAPTER 15. THEOREMS OF STEIN-ROSENBERG TYPE II. OPTIMAL PATHS OF RELAXATION IN THE COMPLEX PLANE
• CHAPTER 16. SPARSE VECTORIZED DIRECT SOLUTION OF ELLIPTIC PROBLEMS
• CHAPTER 17. MULTI-GRID AND ICCG FOR PROBLEMS WITH INTERFACES
• CHAPTER 18. AN AD HOC SIR METHOD
• CHAPTER 19. ON PRECONDITIONED ITERATIVE METHODS FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS
• CHAPTER 20. BLOCK RELAXATION STRATEGIES
• CHAPTER 21. ON THE NUMERICAL SOLUTION OF NONLINEAR ELLIPTIC PDEs ARISING FROM SEMICONDUCTOR DEVICE MODELING
• CHAPTER 22. NON-STANDARD MULTIGRID TECHNIQUES USING CHECKERED RELAXATION AND INTERMEDIATE GRIDS
• CHAPTER 23. SOME EXPERIMENTS IN SOLVING STIFF OSCILLATORY ORDINARY DIFFERENTIAL EQUATIONS
• CHAPTER 24. A NUMERICAL METHOD FOR SOLVING ELLIPTIC BOUNDARY VALUE PROBLEMS IN UNBOUNDED DOMAINS
• CHAPTER 25. APPLICATIONS OF TRANSFINITE ("BLENDING-FUNCTION") INTERPOLATION TO THE APPROXIMATE SOLUTION OF ELLIPTIC PROBLEMS
• CHAPTER 26. APPLICATION OF A PARALLEL PROCESSOR TO THE SOLUTION OF FINITE DIFFERENCE PROBLEMS
• CHAPTER 27. VECTOR ALGORITHMS FOR ELLIPTSC PARTIAL DIFFERENTIAL EQUATIONS BASED ON THE JACOBI METHOD
• CHAPTER 28. ADAPTING ITERATIVE ALGORITHMS DEVELOPED FOR SYMMETRIC SYSTEMS TO NONSYMMETRIC SYSTEMS
• CHAPTER 29. COMPARISON OF METHODS OF SOLUTION OF THE FINITE ELEMENT EQUATIONS FOR THE LARGE DISPLACEMENT ANALYSIS OF ARCHES
• CHAPTER 30. MESH GENERATION BY CONFORMAL AND QUASICONFORMAL MAPPINGS
• CHAPTER 31. BLOCK ITERATIVE METHODS
• CHAPTER 32. A MESH - PARAMETER - CONTINUATION METHOD
• CHAPTER 33. CAPACITANCE MATRIX METHODS - A BRIEF SURVEY
• CHAPTER 34. GEM SOLUTIONS OF ELLIPTIC AND MIXED PROBLEMS WITH NON-SEPARABLE 5- AND 9-POINT OPERATORS
• CHAPTER 35. A PARALLEL BLOCK STIEFEL METHOD FOR SOLVING POSITIVE DEFINITE SYSTEMS
• CHAPTER 36. Numerical Solution of Coupled Systems of Partial Differential Equations in One Spatial Variable and Time
• CHAPTER 37. ON THE CHOICE OF DISCRETlZATION FOR SOLVING P.D.E. 'S ON A MULTI-PROCESSOR
• CHAPTER 38. A SOFTWARE PACKAGE FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS
• CHAPTER 39. AN EMPIRICAL INVESTIGATION OF METHODS FOR NONSYMMETRIC LINEAR SYSTEMS
• CHAPTER 40. SEMICONDUCTOR DEVICE SIMULATION
• Index