GetFEM Documentation contents¶

User Documentation
- Introduction
- How to install
- Linear algebra procedures
- MPI Parallelization of GetFEM
  - State of progress of GetFEM MPI parallelization
- Catch errors
- Build a mesh
  - Add an element to a mesh
  - Remove an element from a mesh
  - Simple structured meshes
  - Mesh regions
  - Methods of the getfem::mesh object
  - Using dal::bit_vector
  - Face numbering
  - Save and load meshes
- Build a finite element method on a mesh
  - First level: manipulating fems on specific elements
  - Examples
  - Second level: optional “vectorization/tensorization”
  - Third level: optional linear transformation (or reduction)
  - Obtaining generic mesh_fem’s
  - The partial_mesh_fem object
- Selecting integration methods
  - Methods of the mesh_im object
- Mesh refinement
- Compute arbitrary terms - high-level generic assembly procedures - Generic Weak-Form Language (GWFL)
  - Overview of GWFL
  - Some basic examples
  - Derivation order and symbolic differentiation
  - C++ Call of the assembly
  - C++ assembly examples
  - Script languages call of the assembly
  - The tensors
  - The variables
  - The constants or data
  - Test functions
  - Gradient
  - Hessian
  - Predefined scalar functions
  - User defined scalar functions
  - Derivatives of defined scalar functions
  - Binary operations
  - Unary operators
  - Parentheses
  - Explicit vectors
  - Explicit matrices
  - Explicit tensors
  - Access to tensor components
  - Constant expressions
  - Special expressions linked to the current position
  - Print command
  - Reshape a tensor
  - Trace, Deviator, Sym and Skew operators
  - Nonlinear operators
  - Macro definition
  - Explicit Differentiation
  - Explicit Gradient
  - Interpolate transformations
  - Element extrapolation transformation
  - Evaluating discontinuities across inter-element edges/faces
  - Double domain integrals or terms (convolution - Kernel - Exchange integrals)
  - Elementary transformations
  - Xfem discontinuity evaluation (with mesh_fem_level_set)
  - Storage of sub-expressions in a getfem::im_data object during assembly
- Compute arbitrary terms - low-level generic assembly procedures (deprecated)
  - available operations inside the comp command
  - others operations
- Some Standard assembly procedures (low-level generic assembly)
  - Laplacian (Poisson) problem
  - Linear Elasticity problem
  - Stokes Problem with mixed finite element method
  - Assembling a mass matrix
- Interpolation of arbitrary quantities
  - Basic interpolation
  - Interpolation based on the generic weak form language (GWFL)
- Incorporate new finite element methods in GetFEM
- Incorporate new approximated integration methods in GetFEM
- Level-sets, Xfem, fictitious domains, Cut-fem
  - Representation of level-sets
  - Mesh cut by level-sets
  - Adapted integration methods
  - Cut-fem
  - Discontinuous field across some level-sets
  - Xfem
  - Post treatment
- Tools for HHO (Hybrid High-Order) methods
  - HHO elements
  - Reconstruction operators
  - Stabilization operators
- Interpolation/projection of a finite element method on non-matching meshes
  - mixed methods with different meshes
  - mortar methods
- Compute \(L^2\) and \(H^1\) norms
- Compute derivatives
- Export and view a solution
  - Saving mesh and mesh_fem objects for the Matlab interface
  - Producing mesh slices
  - Exporting mesh, mesh_fem or slices to VTK/VTU
  - Exporting mesh, mesh_fem or slices to OpenDX
- A pure convection method
- The model description and basic model bricks
  - The model object
  - The brick object
  - How to build a new brick
  - How to add the brick to a model
  - Generic assembly bricks
  - Generic elliptic brick
  - Dirichlet condition brick
  - Generalized Dirichlet condition brick
  - Pointwise constraints brick
  - Source term bricks (and Neumann condition)
  - Predefined solvers
  - Example of a complete Poisson problem
  - Nitsche’s method for dirichlet and contact boundary conditions
  - Constraint brick
  - Other “explicit” bricks
  - Helmholtz brick
  - Fourier-Robin brick
  - Isotropic linearized elasticity brick
  - Linear incompressibility (or nearly incompressibility) brick
  - Mass brick
  - Bilaplacian and Kirchhoff-Love plate bricks
  - Mindlin-Reissner plate model
  - The model tools for the integration of transient problems
  - Small sliding contact with friction bricks
  - Large sliding/large deformation contact with friction bricks
- Numerical continuation and bifurcation
  - Numerical continuation
  - Detection of limit points
  - Numerical bifurcation
  - Approximation of solution curves of a model
- Finite strain Elasticity bricks
  - Some recalls on finite strain elasticity
  - Add an nonlinear elasticity brick to a model
  - Add a large strain incompressibility brick to a model
  - High-level generic assembly versions
- Small strain plasticity
  - Theoretical background
  - Flow rule integration
  - Some classical laws
  - Elasto-plasticity bricks
- ALE Support for object having a large rigid body motion
  - ALE terms for rotating objects
  - ALE terms for a uniformly translated part of an object
- Appendix A. Finite element method list
  - Classical \(P_K\) Lagrange elements on simplices
  - Classical Lagrange elements on other geometries
  - Elements with hierarchical basis
  - Classical vector elements
  - Specific elements in dimension 1
  - Specific elements in dimension 2
  - Specific elements in dimension 3
- Appendix B. Cubature method list
  - Exact Integration methods
  - Newton cotes Integration methods
  - Gauss Integration methods on dimension 1
  - Gauss Integration methods on dimension 2
  - Gauss Integration methods on dimension 3
  - Direct product of integration methods
  - Specific integration methods
  - Composite integration methods
- References
GetFEM Tutorial
- Introduction
  - C++, Python, Scilab or Matlab ?
  - Where are demo files ?
- How to install
- Basic Usage of GetFEM
- Example of Thermo-elastic and electrical coupling (simple nonlinear coupled problem, model object, generic assembly, solve and visualization)
- Example of wheel in contact (Assembly between two meshes, transformations, use of fixed size variables)
  - The problem setting
  - Building the program
Description of the Project
- Introduction
- How to contribute / Git repository on Savannah
- The FEM description in GetFEM
- Description of the different parts of the library
- Appendix A. Some basic computations between reference and real elements
- References
Gmm++ Library
- Introduction
- Installation
- Matrix and Vector type provided by Gmm++
- Input and output with Harwell-Boeing and Matrix Market formats
- sub-vectors and sub-matrices
  - row and column of a matrix
- Miscellaneous methods
- Basic linear algebra operations
- Solving triangular systems
- Dense LU decomposition
- Dense QR factorisation, eigenvalues and eigenvectors
- Iterative solvers
- Catch errors
- Interface with BLAS, LAPACK or ATLAS
- Interface with SuperLU
- How to use Gmm++ with QD type (double-double and quad-double)
- First steps with Gmm++
- Deeper inside Gmm++
- How to disable verifications
Octave and MatLab Interfaces
- Introduction
- Installation
- Preliminary
- GetFEM organization
  - Functions
  - Objects
- Examples
- Draw Command reference
- Command reference
- GetFEM OO-commands
Python Interface
- Introduction
- Installation
- Preliminary
- Python GetFEM interface
- Examples
- How-tos
  - Import gmsh mesh
- API reference
  - ContStruct
  - CvStruct
  - Eltm
  - Fem
  - GeoTrans
  - GlobalFunction
  - Integ
  - LevelSet
  - Mesh
  - MeshFem
  - MeshIm
  - MeshImData
  - MeshLevelSet
  - MesherObject
  - Model
  - Precond
  - Slice
  - Spmat
  - Module asm
  - Module compute
  - Module delete
  - Module linsolve
  - Module poly
  - Module util
SciLab Interface
- Introduction
- Installation
- GetFEM organization
  - Functions
  - Objects
- Draw Command reference
- Command reference
How to install from sources on Linux
- Download sources
- Compiling
How to use docker images of python interface
How to install from sources on MacOS X
- Download sources
- Compiling
How to install GetFEM from sources on Windows
- Build with the Python interface
- Build with the Matlab interface
What’s New in GetFEM
- What’s New in GetFEM 5.4.2
- What’s New in GetFEM 5.4.1
- What’s New in GetFEM 5.4
- What’s New in GetFEM 5.3
- What’s New in GetFEM 5.2
- What’s New in GetFEM 5.1
- What’s New in GetFEM 5.0
- What’s New in GetFEM 4.3
- What’s New in GetFEM 4.2
- What’s New in GetFEM 4.1.1
- What’s New in GetFEM 4.1
- What’s New in GetFEM 4.0
- What’s New in GetFEM 3.1
- What’s New in GetFEM 3.0.1
- What’s New in GetFEM 3.0
- What’s New in GetFEM 2.0.2
- What’s New in GetFEM 2.0.1
- What’s New in GetFEM 2.0
- What’s New in GetFEM 1.7
- What’s New in GetFEM 1.6
- What’s New in GetFEM 1.5
- What’s New in GetFEM 1.4
- What’s New in GetFEM 1.3
- What’s New in GetFEM 1.2
- What’s New in GetFEM 1.1
- What’s New in GetFEM 1.0
Documenting
- Style Guide
- reStructuredText Primer
- Additional Markup Constructs
- Differences to the LaTeX markup
Glossary
About these documents
- Contributors to the GetFEM Documentation
Reporting Bugs in GetFEM
Legal information
History and License
Some related links
- Jean Garrigues courses (in french)
- Internet Finite Element Resources
- MUMPS: a MUltifrontal Massively Parallel sparse direct Solver
- SuperLu: Sparse Gaussian Elimination on High Performance Computers
- Some project using GetFEM and/or Gmm++
- Examples of publications based on GetFEM
- An evaluation of Gmm++ performance
GetFEM Mailing Lists
GetFEM in action …
- Generic mesh handling
- Linear elasticity
- Stokes equation
- Helmholtz equation
- Eigenmodes of a structure (thanks to Paolo Bertolo)
- Contact with friction problem (Houari Khenous)
- Xfem cracks in a beam
- A 3D crack, made via level-set
- Large strain
- Shape and topological optimization
- 3D planetary gears
Matlab source code for the tripod
Matlab source code for the Stokes equation example
Matlab source code for the Helmholtz equation example