Multilevel Block Factorization Preconditioners: Matrix-Based Analysis and Algorithms for Solving Finite Element Equations Book

Pt. I Motivation for preconditioning

1 A finite element tutorial 3

2 A main goal 49

Pt. II Block factorization preconditioners

3 Two-by-two matrices and their factorization 55

4 Classical examples of block-factorizations 89

5 Multigrid (MG) 129

6 Topics on algebraic multigrid (AMG) 199

7 Domain decomposition (DD) methods 263

8 Preconditioning nonsymmetric and indefinite matrices 319

9 Preconditioning saddle-point matrices 327

10 Variable-step iterative methods 363

11 Preconditioning nonlinear problems 377

12 Quadratic constrained minimization problems 385

Pt. III Appendices

A Generalized conjugate gradient methods 407

B Properties of finite element matrices : further details 415

C Computable scales of Sobolev norms 457

D Multilevel algorithms for boundary extension mappings 467

E H[superscript 1][subscript 0]-norm characterization 471

F MG convergence results for finite element problems 477

G Some auxiliary inequalities 507

References 513

Index 527