Krylov Subspace Methods with Application in Incompressible Fluid Flow Solvers

Name: Krylov Subspace Methods with Application in Incompressible Fluid Flow Solvers
Brand: Wiley-ISTE
Price: 110.99 EUR
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Iman Farahbakhsh(Autor*in)

Wiley-ISTE (Verlag)

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Erschienen am 10. Juli 2020

256 Seiten

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978-1-119-61869-0 (ISBN)

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Inhalt

Cover
Title Page
Copyright
Contents
List of Figures
List of Tables
Preface
About the Companion Website
Chapter 1 Introduction
1.1 Motivation
1.1.1 Governing Equations
1.1.2 Methods for Solving Flow Equations
1.2 History of Krylov Subspase Methods
1.3 Scope of Book
1.3.1 The General Structure of Solver
1.3.2 Review of Book Content
Chapter 2 Discretization of Partial Differential Equations and Formation of Sparse Matrices
2.1 Introduction
2.2 Partial Differential Equations
2.2.1 Elliptic Operators
2.2.2 Convection-Diffusion Equation
2.3 Finite Difference Method
2.4 Sparse Matrices
2.4.1 Benchmark Problems for Comparing Solvers
2.4.2 Storage Formats of Sparse Matrices
2.4.2.1 Coordinate Format
2.4.2.2 Compressed Sparse Row Format
2.4.2.3 Block Compressed Row Storage Format
2.4.2.4 Sparse Block Compressed Row Storage Format
2.4.2.5 Modified Sparse Row Format
2.4.2.6 Diagonal Storage Format
2.4.2.7 Compressed Diagonal Storage Format
2.4.2.8 Ellpack-Itpack Format
2.4.3 Redefined Matrix-Vector Multiplication
Exercises
Chapter 3 Theory of Krylov Subspace Methods
3.1 Introduction
3.2 Projection Methods
3.3 Krylov Subspace
3.4 Conjugate Gradient Method
3.4.1 Steepest Descent Method
3.4.2 Derivation of Conjugate Gradient Method
3.4.3 Convergence
3.5 Minimal Residual Method
3.6 Generalized Minimal Residual Method
3.7 Conjugate Residual Method
3.8 Bi-Conjugate Gradient Method
3.9 Transpose-Free Methods
3.9.1 Conjugate Gradient Squared Method
3.9.2 Bi-Conjugate Gradient Stabilized Method
Exercises
Chapter 4 Numerical Analysis of Krylov Subspace Methods
4.1 Numerical Solution of Linear Systems
4.1.1 Solution of Symmetric Positive-Definite Systems
4.1.2 Solution of Asymmetric Systems
4.1.3 Solution of Symmetric Indefinite Systems
4.2 Preconditioning
4.2.1 Preconditioned Conjugate Gradient Method
4.2.2 Preconditioning With the ILU(0) Method
4.2.3 Numerical Solutions Using Preconditioned Methods
4.3 Numerical Solution of Systems Using GMRES*
4.4 Storage Formats and CPU-Time
4.5 Solution of Singular Systems
4.5.1 Solution of Poisson's Equation with Pure Neumann Boundary Conditions
4.5.2 Comparison of the Krylov Subspace Methods with the Point Successive Over-Relaxation (PSOR) Method
Exercises
Chapter 5 Solution of Incompressible Navier-Stokes Equations
5.1 Introduction
5.2 Theory of the Chorin's Projection Method
5.3 Analysis of Projection Method
5.4 The Main Framework of the Projection Method
5.4.1 Implementation of the Projection Method
5.4.2 Discretization of the Governing Equations
5.5 Numerical Case Study
5.5.1 Vortex Shedding from Circular Cylinder
5.5.2 Vortex Shedding from a Four-Leaf Cylinder
5.5.3 Oscillating Cylinder in Quiescent Fluid
Exercises
Appendix A Sparse Matrices
A.1 Storing the Sparse Matrices
A.1.1 Coordinate to CSR Format Conversion
A.1.2 CSR to MSR Format Conversion
A.1.3 CSR to Ellpack-Itpack Format Conversion
A.1.4 CSR to Diagonal Format Conversion
A.2 Matrix-Vector Multiplication
A.2.1 CSR Format Matrix-Vector Multiplication
A.2.2 MSR Format Matrix-Vector Multiplication
A.2.3 Ellpack-Itpack Format Matrix-Vector Multiplication
A.2.4 Diagonal Format Matrix-Vector Multiplication
A.3 Transpose Matrix-Vector Multiplication
A.3.1 CSR Format Transpose Matrix-Vector Multiplication
A.3.2 MSR Format Transpose Matrix-Vector Multiplication
A.4 Matrix Pattern
Appendix B Krylov Subspace Methods
B.1 Conjugate Gradient Method
B.2 Bi-Conjugate Gradient Method
B.3 Conjugate Gradient Squared Method
B.4 Bi-Conjugate Gradient Stabilized Method
B.5 Conjugate Residual Method
B.6 GMRES* Method
Appendix C ILU(0) Preconditioning
C.1 ILU(0)-Preconditioned Conjugate Gradient Method
C.2 ILU(0)-Preconditioned Conjugate Gradient Squared Method
C.3 ILU(0)-Preconditioned Bi-Conjugate Gradient Stabilized Method
Appendix D Inner Iterations of GMRES* Method
D.1 Conjugate Gradient Method Inner Iterations
D.2 Conjugate Gradient Squared Method Inner Iterations
D.3 Bi-Conjugate Gradient Stabilized Method Inner Iterations
D.4 Conjugate Residual Method Inner Iterations
D.5 ILU(0) Preconditioned Conjugate Gradient Method Inner Iterations
D.6 ILU(0) Preconditioned Conjugate Gradient Squared Method Inner Iterations
D.7 ILU(0) Preconditioned Bi-Conjugate Gradient Stabilized Method Inner Iterations
Appendix E Main Program
Appendix F Steepest Descent Method
Appendix G Vorticity-Stream Function Formulation of Navier-Stokes Equation
Bibliography
Index
EULA

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