Getfem++ project

• Introduction
• Diagram of the library
• Introduction to the fem description in Getfem++
• • Convex structures
  • Convexes of reference
  • Shape function type
  • Geometric transformations
  • Finite element methods description
• Description of the different parts of the library
• • Gmm++ library
  • • Description
    • State
    • Perspectives
  • Mesh module
  • • Description
    • State
    • Perspectives
  • FEM module
  • • Description
    • State
    • Perspectives
  • CUBATURE module
  • • Description
    • State
    • Perspectives
  • MESHFEM module
  • • Description
    • State
    • Perspectives
  • LEVELSET module
  • • Description
    • State
    • Perspectives
  • MESHIM module
  • • Description
    • State
    • Perspectives
  • INTEGELEM module
  • • Description
    • State
    • Perspectives
  • ASSEMBLE module
  • • Description
    • State
    • Perspectives
  • BRICK module
  • • Description
    • State
    • Perspectives
  • Matlab and Python interfaces
  • • Description
    • State
    • Perspectives
• Global perspectives of structuration, consolidation and growth
• • Namespace changes
  • Basic types used
• Appendix A. Some basic computations between reference and real elements
• • Volume integral
  • Surface integral
  • Derivative computation
  • Second derivative computation
  • Example of elementary matrix
• References

Introduction

The Getfem++ project focuses on the development of a generic finite element library. The goal is to provide a finite element framework which allows to easily build numerical code for the modelisation of system described by partial differential equations (p.d.e.). A special attention is paid to the flexibility of the use of the library in the sense that the switch from a method offered by the library to another is made as easy as possible.

The major point allowing this, compared to traditional finite element codes, is the complete separation between the description of p.d.e. models and finite element methods. Moreover, a separation is made between integration methods (exact or approximated), geometric transformations (linear or not) and finite element methods of arbitrary degrees described on a reference element. Getfem++ can be used to build very general finite elements codes, where the finite elements, integration methods, dimension of the meshes, are just some parameters that can be changed very easily, thus allowing a large spectrum of experimentations. Numerous examples are available in the tests directory of the distribution.

The goal is also to make the addition of new finite element method as simple as possible. For standard method, a description of the finite element shape functions and the type of connection of degrees of freedom on the reference element is sufficient. Extensions are provided for Hermite elements, piecewise polynomial, non-polynomial, vectorial elements and XFem. Examples of predefined available methods are Pk on simplices in arbitrary degrees and dimensions, Qk on parallelepipeds, P1, P2 with bubble functions, Hermite elements, elements with hierarchic basis (for multigrid methods for instance), discontinuous Pk or Qk, XFem, Argyris, HCT, Raviart-Thomas.

The library also includes the usual tools for finite elements such as assembly procedures for classical PDEs, interpolation methods, computation of norms, mesh operations, boundary conditions, post-processing tools such as extraction of slices from a mesh ...

Getfem++ has no meshing capabilities (apart regular meshes, and a not exploitable attempt), hence, in many situations, it is necessary to import meshes. Imports formats currently known by getfem are GiD , GmSH and emc2 mesh files. However, given a mesh, it is possible to refine it automatically.

The aim of the Getfem++ project is not to provide a ready to use finite element code allowing for instance structural mechanics computations with a graphic interface. It is basically a library allowing the build of C++ finite element codes. However, the matlab and python interfaces allows to easily build application coupling the definition of the problem, the finite element methods selection and the graphical post-processing.

The future of the project is to continue to develop the finite element framework, focusing on the following points.

• Background consolidation of the existing modules (with a reflection on the optimal representation of meshes, degrees of freedom, finite element methods ...).
• Developpement of innovating methods.
• Reflection on the optimal way to represent complex p.d.e. models with the maximum of flexibility and reusability. The brick system is a first step in this direction.

The vocation of Getfem++ is to remain a free open source project. The advantage given by the fact to be an open source project is that by proposing a free use, one profits from the experiments of the users who by their tests and the difficulties or bug which they meet make progress the robustness of the algorithms. One also profits from the possible contributions of the users who can find interest to develop new functinalities within the proposed framework. That allows constructive exchanges which clarify the weak points and the strong points of the project.

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