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