Axellson O., Barker V.A. — Finite Element Solution of Boundary Value Problems. Theory and Computation :: Электронная библиотека попечительского совета мехмата МГУ

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Axellson O., Barker V.A. — Finite Element Solution of Boundary Value Problems. Theory and Computation

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Название: Finite Element Solution of Boundary Value Problems. Theory and Computation

Авторы: Axellson O., Barker V.A.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 432

Добавлена в каталог: 31.01.2010

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

Предметный указатель

Preconditioned conjugate gradient method, application to an unsymmetric system      407 413
Preconditioned conjugate gradient method, computer implementation      49—56
Preconditioned conjugate gradient method, convergence of      30 33
Preconditioned conjugate gradient method, transformed versions      53—56 369—373
Preconditioned method of steepest descent      15—18
Preconditioning by incomplete factorization      38—49 (see also Preconditioning by modified incomplete factorization)
Preconditioning by modified incomplete factorization      337—368 370—373
Preconditioning by modified incomplete, algorithm for factorization      344—345
Preconditioning by modified incomplete, convergence of      349—359
Preconditioning matrix      17 30—31
Preconditioning, algorithm for factorization      40—41
Preconditioning, computer implementation      51—52 54—56
Preconditioning, convergence of      48 49
Preconditioning, defect      39 44—46
Preconditioning, preconditioning matrix      48
Preconditioning, stability of factorization      42—44
Primitive stiffness matrix      187 202—203
Principal minor      281 283 294
QR factorization      287—289
Quadratic functional      7—9 67 73 98 145
Quasi-optimal error estimate      152 154—155 240
Range of a functional      2
Rayleigh quotient      37 160
Re-entrant row      286—287
Recursive static condensation      290 301—304
Regularity      117 130 136 243
Relative discretization error      374
Relative rounding error      374
Residual vector      315—316 368—369
Residual vector in multigrid method      393 395
Residual vector, accurate computation of      373—383
Residual vector, transformed      369
Restriction operator      395
Reverse Cuthill — McKee algorithm      276 289
Riesz representation theorem      105
Ritz method, error analysis      151—153
Ritz method, formulation of      146—151
Ritz method, inhomogeneous boundary conditions      150—153
Ritz — Galerkin method      145—162 181 Ritz
Ritz — Galerkin system      153 182—186 232 269
Rounding error      24 232 239 281 308 310—313 317 373—383 387 392
Row sum      42 203—204 341 346
Search direction      10 19
Self-adjoint operator      (see Operator)
Self-adjoint problem      (see Boundary value problem)
Singularity at a corner      241—244 260—262 397
Smoothing      395
Smoothness      (see Regularity)
Sobolev embedding theorem      117 139 170
Sobolev inner product      115—116
Sobolev Norm      115—116
Sobolev semi-inner product      140 223

Sobolev seminorm      118 140
Sobolev space      113—118
Sobolev space, fractional      128 243
Spectral condition number      8
Spectral equivalence bound      339
Spectral radius      32
Spectrally equivalent sets of matrices      338—339
Splitting of a matrix      32
SSOR      34
SSOR preconditioning      50—51 383—384 388—389
SSOR preconditioning, application to finite element systems      328—337 358—359
SSOR preconditioning, computer implementation      49
SSOR preconditioning, convergence of      35—38 328—330
SSOR preconditioning, general      34—38
SSOR preconditioning, preconditioning matrix      34
Stability      312 (see also Gaussian elimination Preconditioning
Standard element mass matrix      235
Static condensation      (see also Recursive static condensation)
Static condensation at element level      290—296
Static condensation at superelement level      296—297
Stationary iterative method      31—33 38 368—369
Stationary point      4 66
Step discontinuity      117 135—136 224 231 241 245 332
Stiffness matrix      148 186—187 202—204
Stiffness matrix, spectral condition number of      232 238—240 313—315
Storage requirement, conjugate gradient method (simple)      23 383—384 388—389
Storage requirement, direct methods      385 388—389
Storage requirement, preconditioning by incomplete factorization      50—52 55—56 383—384 388
Storage scheme, constant bandwidth storage      271
Storage scheme, row-ordered list      50—51 255 304
Storage scheme, variable bandwidth storage      271 286—287 300
Strongly convex functional      58
Substructure      289 296—297
Summation of first-order differences      378—381
Summation of second-order differences      380—383
Superconvergence      231
Superelement      289—290 296—301
Superelement, matrix      296
Superelement, vector      297
Support diagram      252
Symbolic function      121 130—136
Symmetric operator      (see Operator)
Symmetric pivoting      281
Symmetric structure of a matrix      39
Termination criterion      50
Test function      66
Time-dependent problem      385 387
Total relative error      374
Trace inequality      124 128
Two-point Gauss-Legendre formula      (see Numerical integration)
V multigrid cycle      397
W multigrid cycle      397

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