Trottenberg U., Schuller A., Oosterlee C. — Multigrid :: Электронная библиотека попечительского совета мехмата МГУ

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Trottenberg U., Schuller A., Oosterlee C. — Multigrid

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Название: Multigrid

Авторы: Trottenberg U., Schuller A., Oosterlee C.

Аннотация:

Multigrid presents both an elementary introduction to multigrid methods for solving partial differential equations and a contemporary survey of advanced multigrid techniques and real-life applications.Multigrid methods are invaluable to researchers in scientific disciplines including physics, chemistry, meteorology, fluid and continuum mechanics, geology, biology, and all engineering disciplines. They are also becoming increasingly important in economics and financial mathematics.Readers are presented with an invaluable summary covering 25 years of practical experience acquired by the multigrid research group at the Germany National Research Center for Information Technology. The book presents both practical and theoretical points of view.* Covers the whole field of multigrid methods from its elements up to the most advanced applications* Style is essentially elementary but mathematically rigorous* No other book is so comprehensive and written for both practitioners and students.

Язык:

Рубрика: Математика/Численные методы/Численный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 631

Добавлена в каталог: 20.02.2005

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Предметный указатель

$\omega$ -GS-LEX      105 706
$\omega$ -GS-LEX relaxations      105
$\omega$ -GS-RB      116 212 393
$\omega$ -GS-RB smoothers      189
$\omega$ -GS-RB, 3D Poisson equation and      74
$\omega$ -JAC      34 69 90 115 128 132 160 173 201 202 203 207 214 255 284 296
$\omega$ -JAC relaxations      208 255
$\omega$ -JAC relaxations, operator eigenvalues      73
$\omega$ -JAC, iterative solver for Model Problem 1      204
$\omega$ -JAC, parallel properties      195
$\omega$ -JAC, smoothers      73 119 127
$\omega$ -JAC, smoothing factor for      105
$\omega$ -JAC, smoothing operators      89
$\omega$ -JAC, smoothing properties      33—34
$\omega$ -JAC, smoothing schemes      173
$\omega$ -JAC-RB relaxations      301
$\omega$ -Jacobi operators      33
$\omega$ -Jacobi relaxations      85 195 423 431 433 434 526 535 559
$\omega$ -Jacobi relaxations, smoothing properties      30—31 438
$\omega$ -Jacobi steps      527
$\omega$ -Jacobi — Kaczmarz relaxations      128
$\omega$ -Richardson relaxation      552 554
$\theta$ -zebra line relaxations      392
Absorbing boundary conditions (ABC)      588
Adaptive full multigrid      357 361—366
Adaptive full multigrid (FMG)      364—366
Adaptive grids, full multigrid and      365
Adaptive grids, refinements      23 356 357
Adaptive grids, structure      359
Adaptive multigrid      365 380 388
Adaptive multigrid, cycles      357 365 366 372—373 381
Adaptive multigrid, techniques      385
Additive multigrid      225—226 380 561
Additive Schwarz operator      546
Additive subspace (AS) correction methods      534—535 552 553 554 557
Advection-diffusion operator      584
Aerodynamics, dynamic interaction of wing structure and      411
AFAC (asynchronous fast adaptive composite grid method)      373
Agglomeration techniques      212 216
Aggregation-based algebraic multigrid      453 522—528
Aggressive coarsening      476—478 482 484 485 486 489 490 501
Aircraft configuration, steady-state flow around rigid      411
Aircraft design, complicated flow problems      389
Aircraft, numerical simulation of the full flow around      407
Airfoil, computational flow domain around the      382—385
Algebraic conditions      451 467
Algebraic multigrid      see “AMG”
Algebraic smoothing      432—444
Algebraic turbulence models      585
Algebraically smooth error      432 433 434 435 447 448 454 456 458 459 463 473 530
Algebraically smooth error, approximation of      453
Algebraically smooth error, interpretation of      438—444
Algorithms, asymptotically optimal      556
Algorithms, coarsening      458 476 481
Algorithms, parallel efficiency      195 198 206
Algorithms, self-controlling      49
Algorithms, variable symmetric multiplicative      555
Alternating GS line smoother      285
Alternating GS line smoother, symmetric      240
Alternating ILU decompositions      258
Alternating lexicographic line relaxation      276
Alternating line Gauss — Seidel      236 349
Alternating line relaxations      138 143 145 217 393 415 504 515
Alternating line smoothers      138 141 190
Alternating plane relaxations      217 220
Alternating plane smoothing      147
Alternating symmetric line Gauss — Seidel      238 241
Alternating symmetric line smoothers      238 250
Alternating zebra line relaxations      262 392
Alternating zebra line smoothers (azgs)      138 141 404
AMG (algebraic multignd), coarsening      417 420 489
AMG (algebraic multigrid)      227 264 414 415—418 432 444 471 472 484 492 495 497 501 502 515 521
AMG (algebraic multigrid) approaches      41 412 420—422 425 528
AMG (algebraic multigrid) approaches, aggregation-based      453
AMG (algebraic multigrid) as preconditioner      288 459 473 484—485
AMG (algebraic multigrid), advantage of aggregation-type      528
AMG (algebraic multigrid), algorithms      413 472—485
AMG (algebraic multigrid), applications of      472 485—522
AMG (algebraic multigrid), coarse grids and      242
AMG (algebraic multigrid), coarsening algorithm      419 469
AMG (algebraic multigrid), coarsening strategy      417 518
AMG (algebraic multigrid), components      422—425
AMG (algebraic multigrid), convergence and      491
AMG (algebraic multigrid), cycles      515 519 520
AMG (algebraic multigrid), efficiency and robustness in solving second-order elliptic differential equations      485—522
AMG (algebraic multigrid), error reduction of      502
AMG (algebraic multigrid), flexibility of      417 418
AMG (algebraic multigrid), formal structure of      422
AMG (algebraic multigrid), geometric multigrid and      416
AMG (algebraic multigrid), grid terminology      425—426
AMG (algebraic multigrid), inefficient cycles      524
AMG (algebraic multigrid), interpolation      488 489 521 530
AMG (algebraic multigrid), iteration matrix      513
AMG (algebraic multigrid), low order finite elements      192
AMG (algebraic multigrid), low-memory      498
AMG (algebraic multigrid), parallelization of      532
AMG (algebraic multigrid), robustness of      509
AMG (algebraic multigrid), standard      532
AMG (algebraic multigrid), standard coarsening      488 506
AMG (algebraic multigrid), strategies      489
AMG (algebraic multigrid), strengths of      417
AMG (algebraic multigrid), theoretical basis and notation      422—432
AMG (algebraic multigrid), unstructured grids and      191
AMG (algebraic multigrid), V-cycle convergence      469
AMG1R5      417 492 501 510
AMG1R5, interpolation in      481
Ampere’s Law (Maxwell equation)      511
Anisotropic diffusion equation, ILU smoothing for      261
Anisotropic diffusion problems      227 238 286
Anisotropic discrete systems      418
Anisotropic equations      94 131 141—147 254 262 504
Anisotropic grid structures      226
Anisotropic operators      41 121 125 131 216 260 264
Anisotropic problems      96 126 131 132 133 138 142 145 217 228 257 261 262 415 517
Anisotropic problems, Gauss — Seidel-type relaxations and      135
Anisotropic problems, line smoothers and      134
Anisotropic problems, memory requirement for      507
Anisotropic problems, parallel multigrid strategies for      216
Anisotropic problems, special      513—518
Anisotropic refinements      376
Anisotropics      288 402 419 485
Anisotropics, discrete operators      390
Approximate block Gauss elimination methods      532
Arc-length continuation method      398
Artificial pressure      327 328
Artificial viscosity      241
Artificial viscosity, first-order discretizations and      233—234
Asymptotic convergence behavior      99
Asymptotic convergence behavior, two-grid method      83
Asymptotic convergence factors      36 110 305 489
Asymptotic convergence speed      25
Asymptotic multigrid convergence      251
Backward difference formula (BDF)      64
Backward Euler schemes      406 496
Backward line relaxations      250
Backward line relaxations, Gauss — Seidel      237
Baldwin — Lomax model, two-layer      585
Basic multigrid      28—74 130—192
Bi-CGSTAB      283 284 285 484 519 521
Bicubic interpolation      158 361
Bifurcation problems      395
Biharmonic equations      94 290 291 299
Biharmonic equations, decoupled      307
Biharmonic equations, grid generation and      403—404
Biharmonic equations, transformed systems of      400
Biharmonic problems      306 332
Biharmonic systems      289 291 301—306 404
Bilinear forms      542 562
Bilinear interpolation      43 60 87 173 277 295 305 319 322 330 332 362 364
Bilinear interpolation operator      44 70 72 112 272

Bilinear interpolation, coarse-to-fine transfer      94 392
Bilinear interpolation, FW and      88 89 117 153 173 237 241 251 265 266 267 274
Bilinear interpolation, Model Problem 1 and      61
Block ILU decomposition      263
Block iterations      134 143
Block relaxations      138 145 147 589
Block smoothers      96
Block-Jacobi      554
Block-SOR      554
Block-structured applications      342
boundary conditions      7 8 93 94 148 162 167 182 260 290 292 293 301 303—304 313—314 321 326 332 354 368 375 387 408 441 588
Boundary conditions in parallel      797
Boundary conditions, antiperiodic      443 457 512
Boundary conditions, boundaries and      99
Boundary conditions, coarse grid correction and      299
Boundary conditions, discontinuous      246 247 251
Boundary conditions, discrete      165 179 181 306
Boundary conditions, discretization of      405
Boundary conditions, elimination of      12
Boundary conditions, general      21
Boundary conditions, homogeneous      524
Boundary conditions, multigrid treatment      289 296—297
Boundary conditions, noneliminated      9 43 306
Boundary conditions, number of      291
Boundary conditions, numerical treatment      403
Boundary conditions, relaxation of      178
Boundary conditions, singularities      357
Boundary conditions, type of      242
Boundary grid points      66 207
Boundary integral equations      568
Boundary layers      229 409 587
Boundary related difficulties      587
Boundary relaxation      179 587
Boundary value problems      23 179 183 199 331
Boundary value problems, discrete      8—9
Boundary-volume effect      193 207—208 214—215 379 380
Box relaxations      296 326
Box smoothings      320—322 328—330
Box-line relaxations      320—321 329
Box-line smoothings      321 330
Bratu problem      396—397 398 400
Buneman      14 15
Burger’s Equation      375
Cartesian grids      3 5 6 10 45 62 66—67 71 174 200 211 228 247 318 337
Cartesian velocity components      326
Cascadic multigrid      97
Cauchy — Riemann, on staggered grids      576
Cauchy — Schwarz inequalities      551 557 567
Cauchy — Schwarz inequalities, strengthened      548 554
Cell-centered discretizations      62 69 70
Central and upwind differencing      243—244
CFD (computational fluid dynamics)      228 352—354 421 494—503
CFD (computational fluid dynamics) systems, smoothing for special      576
CFD (computational fluid dynamics), top multigrid efficiency (TME) in      573—589
CFL (Courant — Friedrichs — Lewy) condition      64 65 509
CGS-LEX (lexicographic collective Gauss — Seidel) smoothers      348
CGS-type smoothers      348
Chebychev polynomials      255
Checker-board instability      125 313 315—316 326 331
Chimera technique      5
Cholesky factorization, incomplete      284
Cimmino method      128
Coarse grid corrections      28 34 37—39 47 155 157 227 239—243 252 275 282 319 361 362 364 397 589
Coarse grid corrections, adaptive cycle and      372
Coarse grid corrections, analysis      119
Coarse grid corrections, approaches      414
Coarse grid corrections, Galerkin-based      415
Coarse grid corrections, interpolation of      294—295
Coarse grid corrections, LFA and      99
Coarse grid corrections, operators      106 108 253 424 427 445
Coarse grid corrections, principle      16
Coarse grid corrections, problems      249 256
Coarse grid corrections, smoothing and      264—267 416 418 420 424 432 461
Coarse grid corrections, steps      447
Coarse grid corrections, two-grid analysis and      118 119
Coarse grids      16 18 23 31 40 44 45 46 113 120 179 181 186 193 209 220 275 296 318 392 399 459 559 573
Coarse grids, approximations      119 266 288
Coarse grids, choices of      41 42—43
Coarse grids, collective relaxation on      311
Coarse grids, degree of parallelism      196
Coarse grids, examples of      41
Coarse grids, matrices      561
Coarse grids, multigrid and      211—214
Coarse grids, operators      21 42 94 114 392 413 414 429 470
Coarse grids, points      41 69 165 362 363
Coarse grids, principle      16
Coarse grids, problems      273 564 566 567 569
Coarse grids, sequence of      79
Coarse grids, smoothing factors on      310
Coarse-to-fine transfer      94 158 195 295
Coarsening      67 121 142 415 419 421 450 473—478 486 514 515
Coarsening, aggressive      476—478 479 482 484 485 486 489 490 501
Coarsening, complexity      488—489
Coarsening, one-dimensional      507
Coarsening, rapid      453
Coarsening, slow convergence and fast      459
Coarsening, speed of      459 485
Coefficients, changes in size of      504
Coefficients, diffusion      270
Coefficients, discontinuous      357 503—513
Coefficients, drag      350 352
Coefficients, jumping      268—271 272 274 275 276
Coefficients, lift      350
Coefficients, Runge — Kutta      353
Collective Gauss — Seidel y-line relaxations      310
Collective GS-LEX relaxations      304 332
Collective Jacobi iterations      354
Collective line relaxations      306 338
Collective Newton — Gauss — Seidel relaxations      401
Collective point relaxations      332 338
Collective point relaxations, Gauss — Seidel      402
Collective point relaxations, smoothing factors of      328
Collective relaxations      182 302 304 308 310 310 318 348
Collective smoothing methods      307
Collective smoothing, decoupled smoothing vs      310—311
Communication overhead      199 211 212
Compatibility condition, discrete      184
Complexity, coarsening and      488—489
Composite Cartesian grid, conservative finite volume discretization      368
Composite grids      363
Composite grids, adaptive multigrid and      366—373
Composite grids, conservative discretization      369 370
Composite grids, FAC discretization on      366
Compressible Euler equations      343—345 578
Compressible Euler flow      382
Compressible flow around aircraft      410
Compressible flow equations      290
Compressible Navier — Stokes equations      354—355 579
Compressible Navier — Stokes equations for flow around aircraft      408
Compressible, Euler equations      162
Computational fluid dynamics      see “CFD”
Computer program, local fourier analysis      99
Conjugate gradients      14 283 484 528
Conjugate gradients, acceleration by      507
Connections, negative      439 441 456
Connections, positive      441—444 456 478
Conservative discretizations      370 409 573 580 584
Conservative discretizations at interfaces of refinement areas      367—369
Conservative discretizations, finite volume      368 376
Conservative interpolation      369—371
Continuation methods      575
Continuation methods, multigrid and      395—400
Continuity equations      292 312 314 317 320 323 324 331 332 496 508 586
Continuous differential problems      20
Convection equations      2 234
Convection-diffusion equations      2 119 128 227 247—256 282 308 313 314 347 348 353
Convection-diffusion equations, discretizations      228—234 243—248
Convection-diffusion equations, Galerkin coarse grid discretizations      277
Convection-diffusion equations, smoothing factors      236
Convection-diffusion equations, upwind discretizations      234—243 249—253

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