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<html>
<head>
<title>Domain Decomposition: Parallel Multilevel Methods for Elliptic PDES</title>
</head>
<body>
<h1>Domain Decomposition</h1>
<h2>Parallel Multilevel Methods for Elliptic Partial Differential Equations</h2>
<p><a href="http://BarrySmith.github.io">Barry Smith</a>, Petter Bjorstad, and William Gropp</p>
<p>This book presents an easy-to-read discussion of domain decomposition algorithms,
their implementation and analysis. 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. </p>
<p>Cambridge University Press: <a href="http://www.cup.cam.ac.uk">Europe</a>- <a
href="http://www.cup.org">North America</a></p>
<p>ISBN 0-521-49589-X</p>
<h2>Features</h2>
<menu>
<li>Complete descriptions of most standard domain decomposition, multilevel, and multigrid
algorithms. </li>
<li>All algorithms carefully presented using easy-to-understand matrix notation. </li>
<li>Numerical results indicating the fundamental behavior of the algorithms. </li>
<li>Careful development of the convergence theory for these methods written for a wide
audience. </li>
<li>Discussion of parallel implementations of these methods. </li>
</menu>
<h2>Table of Contents</h2>
<menu>
<li>Chapter 1: One Level Algorithms <menu>
<li>1.1 Classical Alternating Schwarz Method </li>
<li>1.2 Approximate Solvers </li>
<li>1.3 Many Subdomains </li>
<li>1.4 Convergence Behavior </li>
<li>1.5 Implementation Issues </li>
<li>1.6 Variational Formulation </li>
</menu>
</li>
<li>Chapter 2: Two Level Algorithms <menu>
<li>2.1 Subdomain Solves Are Not Sufficient </li>
<li>2.2 A Simple Two Level Method </li>
<li>2.3 General Two Level Methods </li>
<li>2.4 Coarse Grid Corrections </li>
<li>2.5 Convergence Behavior </li>
<li>2.6 Implementation Issues </li>
<li>2.7 Fourier Analysis of Two Level Methods </li>
<li>2.8 Variational Formulation </li>
</menu>
</li>
<li>Chapter 3: Multilevel Algorithms <menu>
<li>3.1 Additive Multilevel Schwarz Methods </li>
<li>3.2 Multiplicative Multilevel Schwarz Methods </li>
<li>3.3 Full Multigrid </li>
<li>3.4 Practical Multilevel Methods </li>
<li>3.5 Multilevel Methods as Classical Jacobi and Gauss-Seidel </li>
<li>3.6 Complexity Issues </li>
<li>3.7 Implementation Issues </li>
<li>3.8 Variational Formulation </li>
</menu>
</li>
<li>Chapter 4: Substructuring Methods <menu>
<li>4.1 Direct Substructuring Methods </li>
<li>4.2 The Two Subdomain Case </li>
<li>4.3 Many Subdomains </li>
<li>4.4 Inexact Subdomain Solves </li>
<li>4.5 Implementation Issues </li>
<li>4.6 Variational Formulation </li>
</menu>
</li>
<li>Chapter 5: A Convergence Theory <menu>
<li>5.1 Abstract Convergence Analysis </li>
<li>5.2 Analysis of Standard Methods </li>
<li>5.3 Indefinite and Nonsymmetric Problems </li>
</menu>
</li>
<li>Appendix 1: Preconditioners and Accelerators </li>
<li>Appendix 2: Software for Numerical Parallel Computing </li>
</menu>
<h2>Errata</h2>
<menu>
<li>Page 15, Computational results 1.1.2 In these comparisons alternating Schwarz refers to
alternating Schwarz without a Krylov accelerator while multiplicative Schwarz is (because
the grids match) alternating Schwarz with GMRES acceleration. </li>
<li>Page 34, line 13. "partioning" should be "partitioning". </li>
<li>Page 36, line 4. "Find v_1 \element V_1" should be "Find e_1 \element
V_1". </li>
<li>Page 57, line 24, "A_{h} u = 1/h^{2} (...) u = f" should be "A_{h} u =
1/h (...) u = h f". </li>
<li>Page 58, line 21, "A_{H} = 1/H^{2}(....)" should be A_{H} = 1/H(....)". </li>
<li>Page 99, line 16. "that it helpful" should be "that it is helpful". </li>
<li>Page 103,line 15,"(5 and 20 ..." should be "(5 or 6 and 20 ..."</li>
<li>Page 103,line 19,remove ",but this time"</li>
<li>Page 106 line 15, The sentence beginning "Using this, we see ... u^{(i)}_{B}."
should be removed. </li>
<li>Page 106, Equation (4.1) should NOT have the \tilde{R}_{i} next to the f_{I}^{(i)} </li>
<li>Page 107, line 22. "competely" should be "completely".</li>
<li>Page 113,equation above (4.5) should have a "g" on the right hand side rather
than "f_B" </li>
<li>Page 137,the expression z^{(i)}z^{(i)T}/z^{(i)T}z^{(i)} should be z^{(i)}z^{(i)T}\hat{S}^{(i)}/z^{(i)T}\hat{S}^{(i)}z^{(i)}
because the projection is in the inner product induced by \hat{S}^{(i)}. </li>
<li>Page 153, the symmetric forms of the algorithms only make sense when the operator A and the preconditioners B_i are all symmetric </li>
<li>Page 172, line 16. "Cr^{-2} \sum ..." should be "C \sum r^{-2} ..."
since "r" is a function of the elements being summed over. </li>
<li>Page 220, line 16. "Lois Curfman McInncs" should be "Lois Curfman
McInnes". </li>
<li>Page 224. "Mathew, J. P." should be "Mathew, T. P." </li>
<li>Page 224. "Wheeler, N. F." should be "Wheeler, M. F." </li>
</menu>
</body>
</html>