Part II Implementation - FEniCS Project

More documents

Recommendations

Info

P q (K) – the space of polynomials of degree ≤ q on Kr – the (weak) residual, r(v) = a(v,u h ) − L(v) or r(v) = F(u h ;v)u h – the finite element solution, u h ∈ V hU – the vector of degrees of freedom for u h = ∑ Ni=1 U iφ iu – the exact solution of a variational problem, u ∈ VˆV – the test spaceV – the trial spaceˆV ∗ – the dual test space, ˆV ∗ = V 0V ∗ – the dual trial space, V ∗ = ˆVˆV h – the discrete test spaceV h – the discrete trial spaceφ i – a basis function in V hˆφ i – a basis function in ˆV hφ K i – a basis function in P KΦ i – a basis function in P 0z – the dual solution, z ∈ V ∗T – the mesh, T = {K}Ω – a bounded domain in R d
List of Authors◮ Editor note: Include author affiliations here.◮ Editor note: Sort alphabetically by last name, not first.• Anders Logg• Andy R. Terrel• Bjørn Fredrik Nielsen• Claes Johnson• David B. Davidson• Emil Alf Løvgren• Evan Lezar• Garth N. Wells• Hans Joachim Schroll• Hans Petter Langtangen• Ilmar M. Wilbers• Joakim Sundnes• Johan Hake• Johan Hoffman• Johan Jansson359
Page 1:
Exploration des Dimensions de la Qu
Page 5:
And now that we may give final prai
Page 8 and 9:
3.6.2 A posteriori error analysis .
Page 10 and 11:
II Implementation 10712 DOLFIN: A C
Page 12 and 13:
19.8.1 Effective tree traversal in
Page 14 and 15:
28.8.5 Aeroacoustics . . . . . . .
Page 16 and 17:
39.7 The Euler Equations . . . . .
Page 19:
CHAPTER2A FEniCS TutorialBy Hans Pe
Page 23 and 24:
CHAPTER3The Finite Element MethodBy
Page 25 and 26:
Robert C. Kirby and Anders LoggFigu
Page 27 and 28:
Robert C. Kirby and Anders Logg3.2.
Page 29 and 30:
Robert C. Kirby and Anders Logg3.3.
Page 31 and 32:
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Robert C. Kirby and Anders Loggavai
Page 41 and 42:
Page 43 and 44:
C ∑ KRobert C. Kirby and Anders L
Page 45 and 46:
Robert C. Kirby and Anders Logg(iii
Page 47 and 48:
CHAPTER4Common and Unusual Finite E
Page 49 and 50:
Robert C. Kirby, Anders Logg and An
Page 51 and 52:
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
4.12 SummaryRobert C. Kirby, Anders
Page 67 and 68:
Page 69 and 70:
CHAPTER5Constructing General Refere
Page 71 and 72:
5.2 PreliminariesRobert C. Kirby an
Page 73 and 74:
RESEARCH EXPERIENCE2006 Guest Revie
Page 75:
Robert C. Kirby and Kent-Andre Mard
Page 79 and 80:
Page 81 and 82:
Page 83:
CHAPTER6Finite Element Variational
Page 87:
CHAPTER8Quadrature Representation o
Page 91:
CHAPTER10Discrete Optimization of F
Page 94 and 95:
Parallel Adaptive Mesh Refinement11
Page 96 and 97:
Parallel Adaptive Mesh Refinementel
Page 98 and 99:
Parallel Adaptive Mesh RefinementFi
Page 100 and 101:
Parallel Adaptive Mesh RefinementTh
Page 102 and 103:
Parallel Adaptive Mesh RefinementFi
Page 104 and 105:
Parallel Adaptive Mesh Refinement87
Page 107:
Part IIImplementation107
Page 111:
CHAPTER13FFC: A Finite Element Form
Page 115 and 116:
CHAPTER15FIAT: Numerical Constructi
Page 117 and 118:
Robert C. KirbyAlgorithm 5 Computes
Page 119 and 120:
Robert C. KirbyThis paradigm may al
Page 121 and 122:
Robert C. Kirby15.4.1 Supplemented
Page 123 and 124:
Robert C. KirbyFigure 15.2: The cub
Page 125:
Robert C. Kirbya new PolynomialSet
Page 128 and 129:
Instant: Just-in-Time Compilation o
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 151:
CHAPTER18UFC: A Finite Element Code
Page 154 and 155:
UFL: A Finite Element Form Language
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
Page 190 and 191:
Page 193 and 194:
CHAPTER20Unicorn: A Unified Continu
Page 195 and 196:
Johan Hoffman, Johan Jansson, Nicla
Page 197 and 198:
Page 199 and 200:
Page 201 and 202:
Page 203 and 204:
Page 205:
Page 209:
CHAPTER22Lessons Learnt in Mixed La
Page 213:
CHAPTER23Finite Elements for Incomp
Page 217:
CHAPTER25Image-Based Computational
Page 221 and 222:
CHAPTER27Cerebrospinal Fluid FlowBy
Page 223 and 224:
Susanne Hentschel, Svein Linge, Emi
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
CHAPTER28Turbulent Flow and Fluid-S
Page 241 and 242:
Page 243:
Page 247 and 248:
CHAPTER30Improved Boussinesq Equati
Page 249 and 250:
N. Lopes, P. Pereira and L. Trabuch
Page 251 and 252:
Page 253 and 254:
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Page 263:
CHAPTER31Multiphase Flow Through Po
Page 267 and 268:
CHAPTER33Simulation of Ca 2+ Dynami
Page 269 and 270:
Johan HakeABFigure 33.1: A: A diagr
Page 271 and 272:
Johan HakeBAFigure 33.2: A: State d
Page 273 and 274:
Johan Hake1 from numpy import *2 fr
Page 275 and 276:
Johan Hake1 # Defining the stabiliz
Page 277 and 278:
Johan Hake∆operatorwillreducethet
Page 279 and 280:
Johan HakeFigure 33.6: The figuresh
Page 281 and 282:
Johan HakeThis method basically giv
Page 283 and 284:
Johan HakeFigure 33.7: The figuresh
Page 285 and 286:
Johan HakeFigure 33.9: The figures
Page 287:
Johan Hake1 from diffsim import *2
Page 290 and 291:
Electromagnetic Waveguide Analysist
Page 292 and 293:
Electromagnetic Waveguide Analysisf
Page 294 and 295:
Electromagnetic Waveguide Analysiss
Page 296 and 297:
Electromagnetic Waveguide Analysiss
Page 298 and 299:
Electromagnetic Waveguide Analysist
Page 300 and 301:
Electromagnetic Waveguide AnalysisT
Page 302 and 303:
Electromagnetic Waveguide Analysisd
Page 304 and 305:
Electromagnetic Waveguide Analysis
Page 306 and 307:
Electromagnetic Waveguide AnalysisM
Page 309: CHAPTER35Applications in Solid Mech
Page 313: CHAPTER37Optimal Control ProblemsBy
Page 316 and 317: Automatic Calibration of Deposition
Page 332 and 333: Computational Thermodynamicssolverf
Page 334 and 335: Computational Thermodynamicstific t
Page 336 and 337: Computational Thermodynamicsare com
Page 338 and 339: Computational Thermodynamicsthe mec
Page 340 and 341: Computational ThermodynamicsFigure
Page 342 and 343: Computational Thermodynamicswhere D
Page 344 and 345: Computational Thermodynamicsto intr
Page 346 and 347: Computational Thermodynamics[?] an
Page 348 and 349: Saddle Point Stabilityfor the testi
Page 350 and 351: [AFW07]Douglas N. Arnold, Richard S
Page 352 and 353: [Cou43][CR72][CR73][Dav04]R. Couran
Page 354 and 355: [Mor68][OD96][Ray70][Rit08][RKL08][
Page 357: APPENDIXANotationThe following nota
Page 361 and 362: Index∇, 165instant-clean,136insta
Page 363: Navier-Stokes, 223Newtonian fluid,
show all

Part II Implementation - FEniCS Project

Create successful ePaper yourself

Delete template?

Save as template?