DOLFIN User Manual - FEniCS Project

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DOLFIN User ManualHoffman, Jansson, Logg, Wells3 Linear algebra 253.1 Matrices and vectors . . . . . . . . . . . . . . . . . . . . . . . 253.2 Matrix-free matrices . . . . . . . . . . . . . . . . . . . . . . . 263.3 Linear solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.4 Preconditioning . . . . . . . . . . . . . . . . . . . . . . . . . . 274 The mesh 294.1 Mesh iterators . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.2 Mesh refinement . . . . . . . . . . . . . . . . . . . . . . . . . . 315 Functions 335.1 Basic properties . . . . . . . . . . . . . . . . . . . . . . . . . . 335.1.1 Representation . . . . . . . . . . . . . . . . . . . . . . 345.1.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 345.1.3 Assignment . . . . . . . . . . . . . . . . . . . . . . . . 355.1.4 Components and sub functions . . . . . . . . . . . . . 355.1.5 Output . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.2 Discrete functions . . . . . . . . . . . . . . . . . . . . . . . . . 365.2.1 Creating a discrete function . . . . . . . . . . . . . . . 375.2.2 Accessing discrete function data . . . . . . . . . . . . . 385.2.3 Attaching discrete function data . . . . . . . . . . . . . 385.3 User-defined functions . . . . . . . . . . . . . . . . . . . . . . 394
DOLFIN User ManualHoffman, Jansson, Logg, Wells5.3.1 Creating a sub class . . . . . . . . . . . . . . . . . . . 395.3.2 Specifying a function-pointer . . . . . . . . . . . . . . . 415.3.3 Cell-dependent functions . . . . . . . . . . . . . . . . . 415.4 Time-dependent functions . . . . . . . . . . . . . . . . . . . . 426 Ordinary differential equations 437 Partial differential equations 457.1 Boundary value problems . . . . . . . . . . . . . . . . . . . . . 457.2 Variational formulation . . . . . . . . . . . . . . . . . . . . . . 467.3 Finite elements and FIAT . . . . . . . . . . . . . . . . . . . . 467.4 Compiling the variational form with FFC . . . . . . . . . . . . 477.5 Element matrices and vectors . . . . . . . . . . . . . . . . . . 477.6 Assemble matrices and vectors . . . . . . . . . . . . . . . . . . 487.7 Specifying boundary conditions and data . . . . . . . . . . . . 497.8 Initial value problems . . . . . . . . . . . . . . . . . . . . . . . 508 Nonlinear solver 538.1 Nonlinear functions . . . . . . . . . . . . . . . . . . . . . . . . 538.2 Newton solver . . . . . . . . . . . . . . . . . . . . . . . . . . . 558.2.1 Linear solver . . . . . . . . . . . . . . . . . . . . . . . 558.2.2 Application of Dirichlet boundary conditions . . . . . . 555
Page 1 and 2: DOLFIN User ManualFebruary 24, 2006
Page 3: ContentsAbout this manual 91 Introd
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Page 25 and 26: Chapter 3Linear algebra◮ Develope
Page 29 and 30: Chapter 4The mesh◮ Developer’s
Page 33 and 34: Chapter 5Functions◮ Developer’s
Page 43: Chapter 6Ordinary differential equa
Page 53 and 54: Chapter 8Nonlinear solver◮ Develo
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DOLFIN User ManualHoffman, Jansson,
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Chapter 10The log systemDOLFIN prov
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Bibliography[1] Cygwin, 2005. http:
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v 2 v 0 = (0, 0)DOLFIN User ManualH
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Appendix CContributing codeIf you h
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Appendix DLicenseDOLFIN is licensed
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