Getfem++ User Guide

• Introduction
• How to install
• 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
  • • From getfem file format
    • Import a mesh
• Selecting finite element methods
• • Examples
  • Other methods of the mesh_fem object
  • Obtaining generic mesh_fems
• Selecting integration methods
• • Methods of the mesh_im object
• Mesh refinement
• Linear algebra procedures
• Standard assembly procedures
• • Laplacian (Poisson) problem
  • Linear Elasticity problem
  • Stokes Problem with mixed finite element method
  • Assembling a mass matrix
• Compute arbitrary elementary matrices - generic assembly procedures
• Incorporate new finite element methods in getfem++ 
• Incorporate new approximated integration methods in getfem++ 
• Level-sets, Xfem, fictitious domains
• • Representation of level-sets
  • Mesh cut by level-sets
  • Adapted integration methods
  • Discontinuous field across some level-sets
  • Fictitious domain approach with Xfem
• Support for Xfem methods
• Interpolation of a finite element method on non-matching meshes
• • mixed methods with different meshes
  • mortar methods
• Compute L² and H¹ 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
  • Exporting mesh, mesh_fem or slices to OpenDX
• Interpolation on different meshes
• The model bricks
• • The model state variable
  • Basic properties of a brick
  • Brick parameters
  • generic elliptic brick
  • Source term brick
  • Constraint brick
  • Dirichlet condition brick
  • Example of a complete Poisson problem
  • Predefined solvers
  • Isotropic linearized elasticity brick
  • Qu term brick
  • Helmholtz brick
  • linear incompressibility (or nearly incompressibility) brick
  • Small displacement plasticity brick
  • Contact and friction conditions brick
  • Linearized plate brick
  • Large strain elasticity brick
  • Large strain incompressibility brick
• Parallelization of getfem++ 
• Catch errors
• Example : Laplacian program
• Appendix A. Finite element method list
• • Dof graphical codification
  • Classical P_K Lagrange elements on simplices
  • Classical Lagrange elements on other geometries
  • Elements with hierarchical basis
  • • Hiercarchical elements with respect to the degree
    • Composite elements
    • Hierarchical composite elements
  • Classical vectorial elements
  • • Raviart-Thomas of lowest order elements
    • Nedelec (or Whitney) edge elements
  • Specific elements in dimension 1
  • • GaussLobatto element
    • Hermite element
    • Lagrange element with an additional bubble function
  • Specific elements in dimension 2
  • • Elements with additional bubble functions
    • Non-conforming P₁ element
    • Hermite element
    • Morley element
    • Argyris element
    • Hsieh-Clough-Tocher element
    • A composite C¹ element on quadrilaterals
  • Specific elements in dimension 3
  • • Elements with additional bubble functions
    • Hermite element
• 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
  • Composite integration methods
• References
• Index

Support for Xfem methods

(outdated, to be done again ...)

Xfem are finite element method with a particular enrichment with non-polynomials functions (see [4] for instance). The file getfem/getfem_Xfem.h gives a support for this kind of method. Any (τ-equivalent) valid finite element method can be extended. If pf is a valid descriptor of a finite element method, one can build a Xfem with the declaration

Xfem  xf(pf);

then one adds a global function with

xf.add_function(pXf, pXg, pXh, ind);

where pXf should be a pointer on a type derived from the object virtual_Xfem_func representing the global function, pXg should be a pointer on a type derived from the object virtual_Xfem_grad representing the global function gradient, pXh is an optional parameter (only for fourth order derivative problems) which should be a pointer on a type derived from the object virtual_Xfem_hess representing the global function Hessian and ind is an index which should correspond to this function to identify the degrees of freedom (this should be different for each function added). It is possible to add an arbitrary number of global functions. The total number of degrees of freedom of the Xfem is the number of degrees of freedom of the initial fem times N_f+1 where N_f is the number of global functions added.

If φ_i for i=1..N_d are the basis functions of pf and f_j for j=1..N_f the additional global functions, the basis functions of the Xfem are the basis function φ_i for i=1..N_d and the basis functions f_jφ_i for i=1..N_d and j=1..N_f. From an element to another and for each function f_j, the corresponding degrees of freedom are connected in a same manner as the corresponding degrees of freedom of pf.

Most of the time, one only needs an enrichment on a subset of node of the original element. If it is so, one should a posteriori eliminate the unwanted extra-dofs.