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McCormick S.F. — Multilevel Adaptive Methods for Partial Differential Equations
McCormick S.F. — Multilevel Adaptive Methods for Partial Differential Equations

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Название: Multilevel Adaptive Methods for Partial Differential Equations

Автор: McCormick S.F.


A practical handbook for understanding and using fast adaptive composite grid (FAC) methods for discretization and solution of partial differential equations (PDEs). Contains fundamental concepts.

These so-called FAC are characterized by their use of a composite grid, which is nominally the union of various uniform grids. FAC is capable of producing a composite grid with tailored resolution, and a corresponding solution with commensurate accuracy, at a cost proportional to the number of composite grid points. Moreover, special asynchronous versions of the fast adaptive composite grid methods (AFAC) studied here have seemingly optimal complexity in a parallel computing environment.

Most of the methods treated in this book were discovered only within the last decade, and in many cases their development is still in its infancy. While this book is therefore not meant to be comprehensive, it does provide a theoretical and practical guide to multilevel adaptive methods and relevant discretization techniques. It also contains new material, which is included to fill in certain gaps and to expose new avenues of research. Also, because adaptive refinement seems to demand a lot of attention to philosophical issues, personal perspectives are often brought freely into the discussion.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 162

Добавлена в каталог: 18.10.2010

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Предметный указатель
Asynchronous fast adaptive composite grid method (AFAC)      24 129—148
BEPS method      24
C-level      74
Coarse grid correction      58
Compatibility condition, analytic      14
Compatibility condition, discrete      30
Composite grid      4 24—27 82
Composite grid harmonic      109
Conservation      14 27—31
Control volume finite element method (CVFE)      9 17
Crank — Nicolson method      41
Delayed correction      90
Direct solver      71 97—100
Discrete ellipticity      48
Domain decomposition      93 134
Error, actual      69
Error, algebraic      65
Error, discretization      44 68
Fast adaptive composite grid method (FAC)      8 81—127
Finite volume element method (FVE)      9 17—55
Finite volume method (FV)      17
Full approximation scheme (FAS)      8 66—68 97
Full multigrid (FMG)      68—72
Galerkin, condition      63 107
Galerkin, nonlinear method      66—68 97
Galerkin, operators      61—66
Galerkin, Petrov — Galerkin      44 62
Gauss divergence theorem      18 32 33 44 149
Gauss — Seidel method      58 92
Grid transfer operator      58
Hierarchical basis method      8
Hypercube      73 141
Immediate correction      89
INTERFACE      5 95
Interpolation      59
jacobi      134
Level      4
Level of discretization error      7 70
Level partitioning      137
Linear part      65
load balancing      138
Mesh refinement      8 92
Multigrid method (MG)      57—81
Multilevel adaptive techniques, (MLAT)      8
Nested, grids      58
Nested, iteration      97—100
Nested, regions      94
Overlap      6
Parallel complexity      140
Parallelism, horizontal      130
Parallelism, vertical      130
Patch      4
Patch conformity      24
Planar cavity flow      31—36
potential flow      13 14
Preconditioner      91 133
Quasi-quadradic      38
Quasi-regular      5
Restriction      59
Reynolds number      13 31—36
Richardson's iteration      65 117
Schwarz method      93 134
Self-adaptive techniques      101—103
Singular equation      27—31 61—66
Slave point      5
Time-dependent equation      15 40—43 100—101
Variational conditions      107
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