Andrea Toselli, Olof Widlund — Springer Series in Computational Mathematics :: Электронная библиотека попечительского совета мехмата МГУ

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Andrea Toselli, Olof Widlund — Springer Series in Computational Mathematics

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Название: Springer Series in Computational Mathematics

Авторы: Andrea Toselli, Olof Widlund

Аннотация:

The purpose of this text is to offer a comprehensive and self-contained presentation of some of the most successful and popular domain decomposition methods for partial differential equations. Strong emphasis is put on both algorithmic and mathematical aspects.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 453

Добавлена в каталог: 13.08.2021

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$H(curl; \Omega)$       348 349
$H(curl; \Omega)$ approximation      see Nedelec elements
$H(curl; \Omega)$ preconditioning      271
$H(div; \Omega)$       347
$H(div; \Omega)$ approximation      see Raviart-Thomas elements
$H(div; \Omega)$ preconditioning      271
Affine mapping      371
anisotropic meshes      202 206 215 273
Average operator      134 139 140 151 208
basis functions Lagrangian      373
Block preconditioners      24 235 241 258
Carding inequality      313 364
Cauchy-Schwarz inequalities, strengthened      40
Coarse grid      59 90 219 274 289 314
Coloring      46
Condition number      395
condition number convergence of conjugate gradient      407
condition number of Schur complement      97 202
condition number of stiffness and mass matrix      390
Conjugate gradient      403
Conjugate residual      409
Convection-diffusion problems      311 326
Counting functions      134
counting functions for $H(div; \Omega)$ and $H(curl; \Omega)$       301
counting functions for elasticity      226
counting functions for scalar elliptic problems      134
counting functions for spectral elements      208
Curl      see $H(curl</a></span> <span class=subjpages><a href=

$H(curl</a></span> <span class=subjpages><a href=

\Omega)$"/>
Darcy flows      see porous media
Deville-Mund preconditioner      196
Direct methods      397
Dirichlet-Neumann      8 18 328
Discontinuous Galerkin      82 327
Divergence      see $H(div; \Omega)$
edge elements      see Nedelec elements
eigenvalue problems      335
Eigenvalues      395
elasticity, linear approximation      375
elasticity, linear nearly incompressible      257 366 388
elasticity, linear preconditioning      217
elasticity, linear well-posedness      357
extensions continuous spaces      342
extensions discrete harmonic      see harmonic extensions discrete
Factorizations      397
FETI      131
FETI DP      see dual-primal
FETI dual-primal      160
FETI dual-primal acceptable edge path      172 229
FETI dual-primal analysis      175
FETI dual-primal for elasticity      227
FETI dual-primal three dimensions      167
FETI dual-primal two dimensions      161
FETI for $H(div, \Omega)$ and $H(curl, \Omega)$       304
FETI for convection-diffusion      329
FETI for Helmholtz      332
FETI for porous media      241
FETI for spectral elements      208
FETI for Stokes problems      241
FETI one-level      143
FETI one-level for elasticity      227
FETI one-level nonredundant Lagrange multipliers      150
FETI one-level redundant Lagrange multipliers      156
FETI two subdomains      2 241
Fictitious domain methods      233
Fill-in      398
finite elements spaces      372
finite elements triangulation      see triangulation
floating subdomains      88
Fredholm alternative      364
Friedrichs inequalities      104 343
Galerkin approximations      371
Gauss-Lobatto meshes      194
Gauss-Lobatto points      377
gmres      15 407
Green's formulas      47 349 350
harmonic extensions comparison      264
harmonic extensions for $H(div, \Omega)$ and $H(curl, \Omega)$       290 295
harmonic extensions for elasticity      222
harmonic extensions for porous media      253
harmonic extensions for spectral elements      201
harmonic extensions for Stokes problems      264
harmonic extensions, discrete      96
Helmholtz equation      312 330
Helmholtz equation FETI-H      332
Helmholtz equation overlapping methods      331
Indefinite problems      362
indefinite problems algebraic      407
indefinite problems approximation      375
inexact solvers      36
Interface conditions      see transmission conditions
interface, subdomain      88
interpolant projection      101
interpolant in $H(curl, \Omega)$       384
interpolant in $H(div, \Omega)$       381
interpolant nodal into and from GLL meshes      195
interpolant quasi-interpolant      62
interpolant standard nodal      99 100 112 373
interpolant standard nodal for nonnested meshes      64
interpolation spaces      339 343
inverse inequalities      389
Jump operator      150
Korn inequalities      358
Lax-Milgram lemma      354 363
Lipschitz domain      337
Mass matrix      391
Maxwell’s equations      362
mesh      see triangulation
Mixed methods      see saddle point problems
mortar methods      233
Nedelec elements interpolant      384
Nedelec elements range and kernel of the curl      384
Nedelec elements three dimensions      383

Nedelec elements two dimensions      382
Neumann-Dirichlet      15
Neumann-Neumann      10 16 131
Neumann-Neumann balancing      133 250 265 301
Neumann-Neumann for $H(div, \Omega)$ and $H(curl, \Omega)$       301
Neumann-Neumann for convection-diffusion      328
Neumann-Neumann for elasticity      225
Neumann-Neumann for porous media      250
Neumann-Neumann for spectral elements      208
Neumann-Neumann for Stokes problems      265
Neumann-Neumann two subdomains      10 241
Nonlinear problems      334
nonnested grids      64
optimal, method      9
Optimality      9
optimized interface conditions      333
overlap, definition/small/generous      56
overlapping metho ds      55
overlapping methods alternative coarse problems      75
overlapping methods analysis      67
overlapping methods for $H(div, \Omega)$ and $H(curl, \Omega)$       274
overlapping methods for elasticity      219
overlapping methods for Helmholtz      331
overlapping methods for nonsymmetric or indefinite problems      314
overlapping methods for porous media      255
overlapping methods for spectral elements      198
overlapping methods for Stokes problems      258
overlapping methods local solvers      56
overlapping methods numerical results      73
overlapping methods standard coarse spaces      59
partition of unity coarse spaces      84
partition of unity functions      57 105 204 295
Plane waves      333
Poincare inequalities      104 343
porous media, flows in approximation      389
porous media, flows in preconditioners      239
porous media, flows in well-posedness      367
positive definite problems      353
positive definite problems algebraic      395 403
positive definite problems approximation      374
Preconditioner      401 406 409
Projection      see interpolant
quasi-optimal, method      18
quotient space arguments      60 346
Raviart-Thomas elements      380
Raviart-Thomas elements interpolant      381
Raviart-Thomas elements range and kernel of the divergence      384
Reference element      371
regularity results      369
Richardson method      399
Robin-Robin      328 329
saddle point problems approximation      386
saddle point problems well-posedness      364
Scalability      17
scalable methods      17
scaling arguments      60
Schur complement      5 94 201 244 251 263 290 397
Schur complement application      94
Schur complement application of the inverse      95
Schur complement condition number      97 202
Schur complement Uzawa algorithm      233 237
Schwarz methods additive      37
Schwarz methods alternating      21 27
Schwarz methods convergence theory      39
Schwarz methods definition      35
Schwarz methods hybrid      38 47 137
Schwarz methods implementation      52
Schwarz methods multiplicative      37
Schwarz methods restricted      75
Smoothed aggregation      81
Sobolev spaces definition      337
Sobolev spaces immersions      340
Sobolev spaces traces      341
Sobolev spacesof vector-valued functions      346
spectral elements      376
spectral elements approximations      378
spectral elements interpolant      195 378
spectral elements preconditioners      193
spectral elements spaces      376
Spectral radius      395
Spectrum      see eigenvalues
Steepest descent      402
Steklov-Poincare operator      6
Stiffness matrix      390
Stokes problem finite element approximations      387
Stokes problem preconditioners      257
Stokes problem spectral element approximations      388
Stokes problem well-posedness      366
subdomain partitions nonoverlapping      88
subdomain partitions overlapping      56
substructuring methods for $H(div, \Omega)$ and $H(curl, \Omega)$       288
substructuring methods for linear elasticity      220
substructuring methods for nonsymmetric or indefinite problems      320 327 331 333
substructuring methods for porous media      241
substructuring methods for scalar problems      113 131
substructuring methods for spectral elements      200
substructuring methods for Stokes problems      261
substructuring methods generalities      87
trace operators continuous spaces      341
trace operators in $H(curl, \Omega)$       349 350
trace operators in $H(div, \Omega)$       347
Transmission conditions      2 4 242 245 331 333
Triangulation      371
triangulation quasiuniform      372
triangulation shape-regular      372
Uzawa algorithm      233
Weighted average      average operator
wire basket an extension from      222
wire basket definition      89
wire basket method for $H(curl, \Omega)$       308
wire basket method for elasticity      221
wire basket method for spectral elements      206

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