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E-grāmata: Krylov Subspace Methods with Application in Incompressible Fluid Flow Solvers

(Amirkabir University of Technology (Tehran Polytechnic), Iran)
  • Formāts: PDF+DRM
  • Izdošanas datums: 10-Jul-2020
  • Izdevniecība: John Wiley & Sons Inc
  • Valoda: eng
  • ISBN-13: 9781119618690
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Krylov Subspace Methods with Application in Incompressible Fluid Flow SolversPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 10-Jul-2020
  • Izdevniecība: John Wiley & Sons Inc
  • Valoda: eng
  • ISBN-13: 9781119618690
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"This book is devoted to the implementation of the Krylov subspace methods for solving systems of equations with different types of matrices. The main purpose is providing a resource for student and researchers who want to exploit the nonstationary solvers like Krylov subspace methods in incompressible flow solvers. This book offers the standard main programs and subroutines and guides the reader to develop the Krylov subspace-based solvers for the solution of the set of equations arise from CFD problems. There are applicable main programs and subroutines in appendices, which supports the results that provided through the book. The content is layed out in such a way that prepares the reader to use Krylov subspace methods in incompressible flow solvers"--

A succinct and complete explanation of Krylov subspace methods for solving systems of equations

Krylov Subspace Methods with Application in Incompressible Fluid Flow Solvers is the most current and complete guide to the implementation of Krylov subspace methods for solving systems of equations with different types of matrices.

Written in the simplest language possible and eliminating ambiguities, the text is easy to follow for post-grad students and applied mathematicians alike. The book covers a breadth of topics, including:

  • The different methods used in solving the systems of equations with ill-conditioned and well-conditioned matrices
  • The behavior of Krylov subspace methods in the solution of systems with ill-posed singular matrices
  • Expertly supported with the addition of a companion website hosting computer programs of appendices

The book includes executable subroutines and main programs that can be applied in CFD codes as well as appendices that support the results provided throughout the text. There is no other comparable resource to prepare the reader to use Krylov subspace methods in incompressible fluid flow solvers.

List of Figures
xi
List of Tables
xv
Preface xvii
About the Companion Website xix
1 Introduction
1(12)
1.1 Motivation
1(3)
1.1.1 Governing Equations
2(1)
1.1.2 Methods for Solving Flow Equations
3(1)
1.2 History of Krylov Subspase Methods
4(3)
1.3 Scope of Book
7(6)
1.3.1 The General Structure of Solver
7(3)
1.3.2 Review of Book Content
10(3)
2 Discretization of Partial Differential Equations and Formation of Sparse Matrices
13(18)
2.1 Introduction
13(1)
2.2 Partial Differential Equations
13(3)
2.2.1 Elliptic Operators
14(1)
2.2.2 Convection-Diffusion Equation
15(1)
2.3 Finite Difference Method
16(1)
2.4 Sparse Matrices
17(14)
2.4.1 Benchmark Problems for Comparing Solvers
17(4)
2.4.2 Storage Formats of Sparse Matrices
21(1)
2.4.2.1 Coordinate Format
21(1)
2.4.2.2 Compressed Sparse Row Format
22(1)
2.4.2.3 Block Compressed Row Storage Format
23(1)
2.4.2.4 Sparse Block Compressed Row Storage Format
24(1)
2.4.2.5 Modified Sparse Row Format
25(1)
2.4.2.6 Diagonal Storage Format
25(2)
2.4.2.7 Compressed Diagonal Storage Format
27(1)
2.4.2.8 Ellpack-Itpack Format
28(1)
2.4.3 Redefined Matrix-Vector Multiplication
28(1)
Exercises
29(2)
3 Theory of Krylov Subspace Methods
31(26)
3.1 Introduction
31(1)
3.2 Projection Methods
31(3)
3.3 Krylov Subspace
34(1)
3.4 Conjugate Gradient Method
35(6)
3.4.1 Steepest Descent Method
35(3)
3.4.2 Derivation of Conjugate Gradient Method
38(2)
3.4.3 Convergence
40(1)
3.5 Minimal Residual Method
41(1)
3.6 Generalized Minimal Residual Method
42(2)
3.7 Conjugate Residual Method
44(1)
3.8 Bi-Conjugate Gradient Method
45(2)
3.9 Transpose-Free Methods
47(10)
3.9.1 Conjugate Gradient Squared Method
48(2)
3.9.2 Bi-Conjugate Gradient Stabilized Method
50(4)
Exercises
54(3)
4 Numerical Analysis of Krylov Subspace Methods
57(42)
4.1 Numerical Solution of Linear Systems
57(12)
4.1.1 Solution of Symmetric Positive-Definite Systems
58(6)
4.1.2 Solution of Asymmetric Systems
64(3)
4.1.3 Solution of Symmetric Indefinite Systems
67(2)
4.2 Preconditioning
69(8)
4.2.1 Preconditioned Conjugate Gradient Method
69(2)
4.2.2 Preconditioning With the ILU(O) Method
71(1)
4.2.3 Numerical Solutions Using Preconditioned Methods
72(5)
4.3 Numerical Solution of Systems Using GMRES*
77(1)
4.4 Storage Formats and CPU-Time
78(6)
4.5 Solution of Singular Systems
84(15)
4.5.1 Solution of Poisson's Equation with Pure Neumann Boundary Conditions
84(11)
4.5.2 Comparison of the Krylov Subspace Methods with the Point Successive Over-Relaxation (PSOR) Method
95(1)
Exercises
96(3)
5 Solution of Incompressible Navier-Stokes Equations
99(120)
5.1 Introduction
99(1)
5.2 Theory of the Chorin's Projection Method
100(1)
5.3 Analysis of Projection Method
101(2)
5.4 The Main Framework of the Projection Method
103(6)
5.4.1 Implementation of the Projection Method
104(1)
5.4.2 Discretization of the Governing Equations
104(5)
5.5 Numerical Case Study
109(8)
5.5.1 Vortex Shedding from Circular Cylinder
109(2)
5.5.2 Vortex Shedding from a Four-Leaf Cylinder
111(1)
5.5.3 Oscillating Cylinder in Quiescent Fluid
112(3)
Exercises
115(2)
Appendix A Sparse Matrices
117(1)
A.1 Storing the Sparse Matrices
117(7)
A.1.1 Coordinate to CSR Format Conversion
117(1)
A.1.2 CSR to MSR Format Conversion
118(1)
A.1.3 CSR to Ellpack-Itpack Format Conversion
119(2)
A.1.4 CSR to Diagonal Format Conversion
121(3)
A.2 Matrix-Vector Multiplication
124(3)
A.2.1 CSR Format Matrix-Vector Multiplication
124(1)
A.2.2 MSR Format Matrix-Vector Multiplication
125(1)
A.2.3 Ellpack-Itpack Format Matrix-Vector Multiplication
125(1)
A.2.4 Diagonal Fornjat Matrix-Vector Multiplication
126(1)
A.3 Transpose Matrix-Vector Multiplication
127(1)
A.3.1 CSR Format Transpose Matrix-Vector Multiplication
127(1)
A.3.2 MSR Format Transpose Matrix-Vector Multiplication
127(1)
A.4 Matrix Pattern
128(3)
Appendix B Krylov Subspace Methods
131(1)
B.1 Conjugate Gradient Method
131(4)
B.2 Bi-Conjugate Gradient Method
135(1)
B.3 Conjugate Gradient Squared Method
136(2)
B.4 Bi-Conjugate Gradient Stabilized Method
138(2)
B.5 Conjugate Residual Method
140(2)
B.6 GMRES* Method
142(3)
Appendix C ILU(0) Preconditioning
145(1)
C.1 ILU(0)-Preconditioned Conjugate Gradient Method
145(4)
C.2 ILU(0)-Preconditioned Conjugate Gradient Squared Method
149(2)
C.3 ILU(0)-Preconditioned Bi-Conjugate Gradient Stabilized Method
151(4)
Appendix D Inner Iterations of GMRES* Method
155(1)
D.1 Conjugate Gradient Method Inner Iterations
155(2)
D.2 Conjugate Gradient Squared Method Inner Iterations
157(1)
D.3 Bi-Conjugate Gradient Stabilized Method Inner Iterations
158(2)
D.4 Conjugate Residual Method Inner Iterations
160(2)
D.5 ILU(O) Preconditioned Conjugate Gradient Method Inner Iterations
162(1)
D.6 ILU(O) Preconditioned Conjugate Gradient Squared Method Inner Iterations
163(2)
D.7 ILU(O) Preconditioned Bi-Conjugate Gradient Stabilized Method Inner Iterations
165(2)
Appendix E Main Program
167(6)
Appendix F Steepest Descent Method
173(4)
Appendix G Vorticity-Stream Function Formulation of Navier-Stokes Equation
177(42)
Bibliography 219(6)
Index 225
IMAN FARAHBAKHSH, Ph.D., is an Assistant Professor of Hydromechanics and Propulsion Systems in the Department of Maritime Engineering at the Amirkabir University of Technology. His research interests lie in the area of computational fluid dynamics, fluid-structure interaction, multiphase flow, instability in fluids, and numerical linear algebra. The present book is the result of more than a decade of his studies in computational mathematics and application of Krylov subspace methods in CFD codes and the development of computer programs.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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