%0 Book %1 brandt2011multigrid %A Brandt, Achi %A Livne, Oren E. %D 2011 %I Society for Industrial and Applied Mathematics %K PDE computation multigrid numerical_methods review %R 10.1137/1.9781611970753 %T Multigrid Techniques %U http://epubs.siam.org/doi/abs/10.1137/1.9781611970753 %X The Multigrid Guide presents the best known practices and techniques for devel- oping multigrid solvers. As best practices evolve with on-going developments, the history of the Guide mirrors the history of the field of multigrid research. We de- lineate between two eras that must be born in mind when reading this book: 1984 and earlier, and 1984 to present time. The earlier period (summarized in the 1984 Guide). Parts I and II of that Guide were based on Bra82b, the first being an expansion of an even ear- lier mini-guide Bra80c. The present Classics Edition of the 1984 Guide includes quite a few minor corrections, additional comments and clarifications of the original manuscript; still, it overall describes the state-of-the-art of multigrid as of 1984 and cites other works of that time. Multigrid solvers for discretized elliptic partial differ- ential equations on well-structured grids, including various CFD systems, are well represented, as they had already matured at that time; but later important multi- grid developments are absent. To maintain consistency with the rest of the book, the Introduction (§0) has not been updated; so “recent” developments referenced therein are now nearly thirty years old. Equipped with the hindsight of contemporary research, yet faithful to the spirit of the 1984 Guide, only few essential modifications were made. Chapter 14 was thoroughly revised to emphasize general solver performance predictors rather than Local Mode Analysis (LMA). In the early days, the latter was the best approach to practical quantitative performance analysis, hence it is extensively used throughout the entire Part I of this book. While LMA predictions are still perfectly valid today, the new predictors are simpler and preferable in many circumstances. Additionally, • The original CycleV model Fortran program was replaced with a modern object-oriented Matlab program in §1.5 and App. A. • The local relaxation rule of §5.7 and its FMG application (§9.6) were added. • The proper usage of a large cycle index, including fractional values, is now explained in §6.2. Recent Developments (1984 to present). We caution the reader that this edition of the Guide falls short of representing later multigrid developments. We regard this book as a baseline for the future Multigrid Guide 2.0 project, which will be continuously updated to match contemporary research and literature. The 2.0 project is accessible online at http://www.siam.org/books/cl67.

@book{brandt2011multigrid, abstract = {The Multigrid Guide presents the best known practices and techniques for devel- oping multigrid solvers. As best practices evolve with on-going developments, the history of the Guide mirrors the history of the field of multigrid research. We de- lineate between two eras that must be born in mind when reading this book: 1984 and earlier, and 1984 to present time. The earlier period (summarized in the 1984 Guide). Parts I and II of that Guide were based on [Bra82b], the first being an expansion of an even ear- lier mini-guide [Bra80c]. The present Classics Edition of the 1984 Guide includes quite a few minor corrections, additional comments and clarifications of the original manuscript; still, it overall describes the state-of-the-art of multigrid as of 1984 and cites other works of that time. Multigrid solvers for discretized elliptic partial differ- ential equations on well-structured grids, including various CFD systems, are well represented, as they had already matured at that time; but later important multi- grid developments are absent. To maintain consistency with the rest of the book, the Introduction (§0) has not been updated; so “recent” developments referenced therein are now nearly thirty years old. Equipped with the hindsight of contemporary research, yet faithful to the spirit of the 1984 Guide, only few essential modifications were made. Chapter 14 was thoroughly revised to emphasize general solver performance predictors rather than Local Mode Analysis (LMA). In the early days, the latter was the best approach to practical quantitative performance analysis, hence it is extensively used throughout the entire Part I of this book. While LMA predictions are still perfectly valid today, the new predictors are simpler and preferable in many circumstances. Additionally, • The original CycleV model Fortran program was replaced with a modern object-oriented Matlab program in §1.5 and App. A. • The local relaxation rule of §5.7 and its FMG application (§9.6) were added. • The proper usage of a large cycle index, including fractional values, is now explained in §6.2. Recent Developments (1984 to present). We caution the reader that this edition of the Guide falls short of representing later multigrid developments. We regard this book as a baseline for the future Multigrid Guide 2.0 project, which will be continuously updated to match contemporary research and literature. The 2.0 project is accessible online at http://www.siam.org/books/cl67.}, added-at = {2014-11-04T07:33:29.000+0100}, author = {Brandt, Achi and Livne, Oren E.}, biburl = {https://www.bibsonomy.org/bibtex/2c94d14dd8b010b918a9eeb32aa7dec76/peter.ralph}, doi = {10.1137/1.9781611970753}, eprint = {http://epubs.siam.org/doi/pdf/10.1137/1.9781611970753}, interhash = {82b86ad9f38ecdf0b8f0490b546db1d9}, intrahash = {c94d14dd8b010b918a9eeb32aa7dec76}, keywords = {PDE computation multigrid numerical_methods review}, publisher = {Society for Industrial and Applied Mathematics}, timestamp = {2014-11-04T07:33:29.000+0100}, title = {Multigrid Techniques}, url = {http://epubs.siam.org/doi/abs/10.1137/1.9781611970753}, year = 2011 }