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 |  موضوع: كتاب Design of Adaptive Finite Element Software الجمعة 15 أغسطس 2014, 5:57 pm | |
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Design of Adaptive Finite Element Software - Alfred Schmidt & Kunibert G. Siebert
Editors
Timothy J. Barth, Moffett Field, CA
Michael Griebel, Bonn
David E. Keyes, New York
Risto M. Nieminen, Espoo
Dirk Roose, Leuven
Tamar Schlick, New York
ويتناول الموضوعات الأتية :
Introduction 1
1 Concepts and abstract algorithms 9
11 Meshrefinement andcoarsening 9
111 Refinement algorithms for simplicial meshes 12
112 Coarsening algorithm for simplicial meshes18
113 Operations during refinement and coarsening 20
12 Thehierarchicalmesh 22
13 Degreesof freedom 24
14 Finite element spaces and finite element discretization 25
141 Barycentriccoordinates 26
142 Finiteelement spaces 29
143 Evaluationof finiteelement functions 29
144 Interpolation and restriction during refinement and
coarsening 32
145 Discretizationof 2ndorder problems 35
146 Numericalquadrature 38
147 Finite element discretization of 2nd order problems39
15 AdaptiveMethods 42
151 Adaptive method for stationaryproblems 42
152 Meshrefinementstrategies 43
153 Coarseningstrategies 47
154 Adaptive methods for time dependent problems 49
2 Implementation of model problems 55
21 Poissonequation 56
211 Include file andglobalvariables 56
212 The main program for the Poisson equation57
213 The parameter file for the Poissonequation 59
214 Initializationof thefiniteelement space 60
215 Functions for leaf data 60
XContents
216 Data of the differentialequation 62
217 The assemblageof the discretesystem 63
218 Thesolutionof thediscretesystem 65
219 Errorestimation 66
22 Nonlinear reaction–diffusionequation 68
221 Program organization and header file 69
222 Globalvariables 71
223 The main program for the nonlinear reaction–diffusion
equation 71
224 Initialization of the finite element space and leaf data 72
225 Thebuildroutine 72
226 Thesolveroutine 73
227 Theestimatorfor thenonlinear problem 73
228 Initializationof problemdependent data 75
229 The parameter file for the nonlinear reaction–diffusion
equation 79
2210 Implementation of the nonlinear solver80
23 Heat equation 93
231 Globalvariables 93
232 The main program for the heat equation 94
233 The parameter file for the heat equation 96
234 Functions for leaf data 98
235 Data of the differentialequation 99
236 Timediscretization100
237 Initialdata interpolation 100
238 The assemblageof the discretesystem 101
239 Errorestimation 105
2310 Timesteps 107
24 Installation ofALBERTAand fileorganization111
241 Installation111
242 Fileorganization 111
3 Data structures and implementation113
31 Basic types, utilities, and parameter handling113
311 Basictypes 113
312 Messagemacros114
313 Memoryallocationanddeallocation 118
314 Parametersandparameter files122
315 Parameters used by the utilities 127
316 Generating filenames for meshes and finite element
data 127
32 Data structures for the hierarchicalmesh 128
321 Constants describing the dimension of the mesh 128
322 Constants describing the elements of the mesh 129
323 Neighbour information 129
Contents XI
324 Elementindices 130
325 TheBOUNDARYdata structure 130
326 Thelocalindexing onelements132
327 TheMACROELdata structure132
328 TheELdata structure134
329 TheELINFOdata structure135
3210 TheNEIGH, OPPVERTEXandELTYPEmacros137
3211 TheINDEXmacro137
3212 TheLEAFDATAINFOdata structure 138
3213 TheRCLISTELdata structure140
3214 TheMESHdata structure 141
3215 Initializationof meshes 143
3216 Reading macrotriangulations 144
3217 Writing macrotriangulations 150
3218 Import and export of macro triangulations from/to
other formats 151
3219 Meshtraversalroutines 153
33 Administrationof degreesof freedom161
331 TheDOFADMINdata structure 162
332 Vectors indexed by DOFs: TheDOF*VECdata
structures 164
333 Interpolation and restriction of DOF vectors during
meshrefinementandcoarsening167
334 TheDOFMATRIXdata structure 168
335 Access to global DOFs: Macros for iterations using
DOFindices 170
336 Access to local DOFs on elements171
337 BLAS routines for DOF vectors and matrices 173
338 Reading and writing of meshes and vectors173
34 The refinement andcoarsening implementation176
341 Therefinementroutines176
342 Thecoarseningroutines 182
35 Implementationof basis functions 183
351 Data structures for basis functions184
352 Lagrangefiniteelements190
353 Piecewise constant finite elements191
354 Piecewise linear finite elements 191
355 Piecewise quadratic finite elements 195
356 Piecewise cubic finite elements 200
357 Piecewise quartic finite elements 204
358 Access to Lagrange elements 206
36 Implementationof finite element spaces 206
361 The finite element space data structure 206
362 Access to finite element spaces 207
37 Routines for barycentriccoordinates 208
XII Contents
38 Data structures for numericalquadrature210
381 TheQUADdata structure 210
382 TheQUADFASTdata structure 212
383 Integration over sub–simplices (edges/faces) 215
39 Functions for theevaluationof finiteelements216
310 Calculation of norms for finite element functions 221
311 Calculation of errors of finite element approximations222
312 Tools for the assemblageof linear systems 224
3121 Assembling matrices and right hand sides 224
3122 Data structures and function for matrix assemblage227
3123 Data structures for storing pre–computed integrals of
basis functions 236
3124 Data structures and functions for vector update 243
3125 Dirichlet boundary conditions247
3126 Interpolationinto finite element spaces248
313 Data structures and procedures for adaptive methods249
3131ALBERTAadaptive method for stationary problems249
3132 StandardALBERTAmarking routine255
3133ALBERTAadaptive method for time dependent
problems 256
3134 Initialization of data structures for adaptive methods 260
314 Implementationof errorestimators 263
3141 Error estimator for elliptic problems 263
3142 Error estimator for parabolic problems266
315 Solverfor linear andnonlinearsystems 268
3151 Generallinear solvers 268
3152 Linear solvers for DOF matrices and vectors 272
3153 Access of functions for matrix–vector multiplication 274
3154 Access of functions for preconditioning275
3155 Multigridsolvers 277
3156 Nonlinear solvers282
316 Graphics output285
3161 One and two dimensional graphics subroutines 286
3162 gltools interface 290
3163 GRAPEinterface293
References295
Index301
Data types, symbolic constants, functions, and macros311
Data types 311
Symbolicconstants311
Functions 312
Macros
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