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