349
edits
Summer of Code - Getting Started: Difference between revisions
→General purpose library Finite Element library
(→Octave-Forge packages: minor typo) |
|||
| Line 39: | Line 39: | ||
Octave-Forge already has a set of packages for discretizing Partial Differential operators by Finite Elements and/or Finite Volumes, | Octave-Forge already has a set of packages for discretizing Partial Differential operators by Finite Elements and/or Finite Volumes, | ||
namely the [[bim package]] which relies on the [http://octave.sf.net/msh msh package] (which is in turn based on [http://geuz.org/gmsh/ gmsh]) for creating and managing 2D triangular and 3D tetrahedral meshes and on the [http://octave.sf.net/fpl fpl package] for visualizing 2D results within Octave or exporting 2D or 3D results in a format compatible with [http://www.paraview.org Paraview] or [https://wci.llnl.gov/codes/visit/ VisIT]. These packages, though, offer only a limited choice of spatial discretization methods which are based on low degree polynomials and therefore have a low order of | namely the [[bim package]] which relies on the [http://octave.sf.net/msh msh package] (which is in turn based on [http://geuz.org/gmsh/ gmsh]) for creating and managing 2D triangular and 3D tetrahedral meshes and on the [http://octave.sf.net/fpl fpl package] for visualizing 2D results within Octave or exporting 2D or 3D results in a format compatible with [http://www.paraview.org Paraview] or [https://wci.llnl.gov/codes/visit/ VisIT]. These packages, though, offer only a limited choice of spatial discretization methods which are based on low degree polynomials and therefore have a low order of accuracy even for problems with extremely smooth solutions. | ||
The [http://geopdes.sf.net GeoPDEs] project, on the other hand, offers a complete suite of functions for discretizing a wide range of | The [http://geopdes.sf.net GeoPDEs] project, on the other hand, offers a complete suite of functions for discretizing a wide range of | ||
differential operators related to important physical problems and uses basis functions of arbitrary polynomial degree that allow the construction of methods of high accuracy. These latter, though, are based on the IsoGeometric Analysis Method which, although very powerful and often better performing, is less widely known and adopted than the Finite Elements Method. The implementation of a general purpose library of Finite Elements seems therefore a valuable addition to Octave-Forge. Two possible interesting choices for implementing this package exist, the first consists of implementing the most common Finite Element spaces in the [http://geopdes.sf.net GeoPDEs] framework, which is possible as IsoGeometric Analysis can be viewed as a superset of the Finite Element Method, the other is to construct Octave language bindings for the free software library [http://fenicsproject.org/documentation/ FEniCS] based on the existing C++ or Python interfaces. | differential operators related to important physical problems and uses basis functions of arbitrary polynomial degree that allow the construction of methods of high accuracy. These latter, though, are based on the IsoGeometric Analysis Method which, although very powerful and often better performing, is less widely known and adopted than the Finite Elements Method. The implementation of a general purpose library of Finite Elements seems therefore a valuable addition to Octave-Forge. Two possible interesting choices for implementing this package exist, the first consists of implementing the most common Finite Element spaces in the [http://geopdes.sf.net GeoPDEs] framework, which is possible as IsoGeometric Analysis can be viewed as a superset of the Finite Element Method, the other is to construct Octave language bindings for the free software library [http://fenicsproject.org/documentation/ FEniCS] based on the existing C++ or Python interfaces. | ||