Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential EquationsCambridge University Press, 2004-03-25 - 240 psl. This book presents an easy-to-read discussion of domain decomposition algorithms, their implementation and analysis. The relationship between domain decomposition and multigrid methods is carefully explained at an elementary level, and discussions of the implementation of domain decomposition methods on massively parallel super computers are also included. All algorithms are fully described and explained, and a mathematical framework for the analysis and complete understanding of the methods is also carefully developed. In addition, numerous numerical examples are included to demonstrate the behaviour of this important class of numerical methods. This book is ideal for graduate students about to embark on a career in computational science. It will also be a valuable resource for all those interested in parallel computing and numerical computational methods. |
Turinys
One Level Algorithms | 1 |
12 Approximate Solvers | 18 |
13 Many Subdomains | 19 |
14 Convergence Behavior | 24 |
15 Implementation Issues | 30 |
16 Variational Formulation | 34 |
Two Level Algorithms | 41 |
22 A Simple Two Level Method | 43 |
37 Implementation Issues | 98 |
38 Variational Formulation | 100 |
Substructuring Methods | 101 |
42 The Two Subdomain Case | 110 |
43 Many Subdomains | 124 |
44 Inexact Subdomain Solvers | 141 |
45 Implementation Issues | 144 |
A Convergence Theory | 149 |
23 General Two Level Methods | 45 |
24 Coarse Grid Corrections | 48 |
25 Convergence Behavior | 49 |
26 Implementation Issues | 53 |
27 Fourier Analysis of Two Level Methods | 57 |
28 Variational Formulation | 61 |
Multilevel Algorithms | 67 |
32 Multiplicative Multilevel Schwarz Methods | 76 |
33 Full Multigrid | 85 |
34 Practical Multilevel Methods | 87 |
35 Multilevel Methods as Classical Jacob and GaussSeidel | 89 |
36 Complexity Issues | 91 |
52 Abstract Convergence Analysis | 153 |
53 Analysis of Standard Methods | 161 |
54 Indefinite and Nonsymmetric Problems | 185 |
Preconditioners and Accelerators | 195 |
Krylov Subspace Methods | 197 |
Software for Numerical Parallel Computing | 201 |
A22 Abstract Data Types | 204 |
A23 Our Standard Model for Parallel Computing | 207 |
| 209 | |
| 223 | |
Kiti leidimai - Peržiūrėti viską
Pagrindiniai terminai ir frazės
additive Schwarz method alternating Schwarz method analysis apply approximate artificial boundary Assumption bilinear form block calculated coarse grid correction coarse grid problem coefficients color condition number conjugate gradient convergence behavior convergence rate define denote Dirichlet boundary conditions discussion domain decomposition algorithms domain decomposition methods Dryja edge eigenvalues elliptic PDEs equations error Figure functions Gauss-Seidel given GMRES hierarchical basis implementation interior interpolation introduced iteration count Jacobi Krylov subspace method Lemma level methods linear system mesh multigrid methods multilevel diagonal scaling multilevel methods multilevel Schwarz multiplicative Schwarz method nodes Notes and References null space number of iterations number of subdomains obtain operator overlapping Schwarz methods parallel computers partitioning Poisson problem preconditioned preconditioner processors programming proof References for Section restriction Schur complement simple solution solve sparse matrix subdomain solver subdomains symmetric term three dimensions triangulation un+1 V-cycle vector vertex space zero
Populiarios ištraukos
217 psl. - In Roland Glowinski, Gene H. Golub, Gerard A. Meurant, and Jacques Periaux, editors, First International Symposium on Domain Decomposition Methods for Partial Differential Equations, Philadelphia, PA, 1988.
211 psl. - In David E. Keyes, Tony f. Chan, Gerard A. Meurant, Jeffrey S. Scroggs, and Robert G. Voigt, editors, Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, 19-36, Philadelphia, PA, (1992).
217 psl. - Two-level domain decomposition preconditioning for the pversion finite element version in three dimensions', Int. J. Numer. Meth.
209 psl. - K. BELL, B. HATLESTAD, OE HANSTEEN, AND PO ARALDSEN, NORSAM, a programming system for the finite element method. Users manual, Part 1, General description., NTH, Trondheim, 1973.
216 psl. - A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation, SIAM J.
218 psl. - Nepomnyaschikh. On the application of the method of bordering for elliptic mixed boundary value problems and on the difference norms of W2 (S).
218 psl. - Oswald. Multilevel Finite Element Approximation, Theory and Applications. Teubner Skripten zur Numerik.
220 psl. - Smith, A domain decomposition algorithm for elliptic problems in three dimensions, Numer. Math. 60 (1991) 219-234.