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

Selecting integration methods

The description of an integration method on a whole mesh is done thanks to the structure getfem::mesh_im, defined in the file getfem/getfem_mesh_im.h. Basically, this structure describes the integration method on each element of the mesh. One can instantiate a getfem::mesh_im object as follows

 getfem::mesh_im mim(mymesh);

where mymesh is an already existing mesh. The structure will be linked to this mesh and will react when modifications will be done on it (for example when the mesh is refined, the integration method will be also refined).

It is possible to specify element by element the integration method, so that element of mixed types can be treated, even if the dimensions are different.

To select a particular integration method on a given element, one can use
  mf.set_integration_method(i, ppi);
where i is the index of the element and ppi is the descriptor of the integration method. Alternative forms of this member function are:

void mesh_fem::set_integration_method(const dal::bit_vector &cvs, 
  getfem::pintegration_method ppi);
void mesh_fem::set_integration_method(getfem::pintegration_method ppi);

which set the integration method for either the convexes listed in the bit_vector cvs, or all the convexes of the mesh.

The list of all available descriptors of integration methods is in the file getfem/getfem_integration.h.
Descriptors for integration methods are available thanks to the following function:  

getfem::pintegration_method ppi = 
          getfem::int_method_descriptor("name of method");

where "name of method" is to be chosen among the existing methods. A name of a method can be retrieved with

std::string im_name = getfem::name_of_int_method(ppi);

A non exhautive list (see Appendix B or getfem/getfem_integration.h for exhaustive lists) of integration methods is given below.

Examples of exact integration methods:

An alternative way to obtain integration methods:  

getfem::pintegration_method 
  getfem::classical_exact_im(bgeot::pgeometric_trans pgt);
getfem::pintegration_method 
  getfem::classical_approx_im(bgeot::pgeometric_trans pgt, dim_type d);

These functions return an exact (i.e. analytical) integration method, or select an approximate integration method which is able to integrate exactly polynomials of degree <= d (at least) for convexes defined with the specified geometric transformation.

Methods of the mesh_im object

Once an integration method is defined on a mesh, it is possible to obtain information on it with the following methods (the list is not exhaustive).