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

Parallelization of getfem++ 

Of course, each different problem should require a different parallelization adapted to its specificities. You may build your own parallelization using the mesh regions to parallelize assembly procedures.

Nevertheless, the brick system offers a generic parallelization based on MPI (communication between processes), METIS (partition of the mesh) and MUMPS (parallel sparse direct solver). One has to compile getfem++ with the option "-D GETFEM_PARA_LEVEL=2" to use it. With this option, each mesh used is implicitely partitionned (using METIS) into a number of regions corresponding to the number of processors and the assembly procedures are parallelized. This means that the tangent matrix and the constraint matrix assembled in the model_state variable are distributed. The choice made (for the moment) is not to distribute the vectors. So that the right hand side vectors in the model_state variable are communicated to each processor (the sum of each contribution is made at the end of the assembly and each processor has the complete vector). note that you have to think to the fact that the matrices stored by the bricks are all distributed.

Concerning the constraints, it is preferable for a better parallelization to avoid the getfem::ELIMINATED_CONSTRAINTS option (i.e. not to use the constraint matrix).

A model of parallelized program is elastostatic.cc in the directory tests of the distribution.

The following functions are also implicitely parallelized using the option "-D GETFEM_PARA_LEVEL=2":

• computation of norms (asm_L2_norm, asm_H1_norm, asm_H2_norm ..., in getfem/getfem_assembling.h),
• asm_mean_value (in getfem/getfem_assembling.h),
• error_estimate (in getfem/getfem_error_estimate.h).

This means that these functions have to be called on each processor.

Parallelization of getfem is still considered a "work in progress"..

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