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Section Navigation

  • XLiFE++’s basics
    • Basic types
    • Vectors and matrices
    • Functions and kernels
    • Global variables and parameters
    • Main user’s classes of XLiFE++
    • C++ syntax
    • The key-value system
      • Keys for mandatory init
      • Keys for geometries
      • Keys for transformations
      • Keys for meshes
      • Keys for spaces
      • Keys for unknowns
      • Keys in forms
      • Keys for integration methods
      • Keys for terms
      • Keys for solvers
      • Keys for visualization
  • Maths resources
    • Polynomials and random generators
    • Integration and ODE
    • Special functions and Green’s kernels
    • Splines
    • Parametrizations
    • Geometrical transformations
  • Geometry definition
    • Segment
    • Elliptical and circular arcs
    • ParametrizedArc
    • SplineArc
    • Polygon
      • Triangle
      • Quadrangle
      • Parallelogram
      • Rectangle
      • SquareGeo
    • Ellipses & disks
    • ParametrizedSurface
    • SplineSurface
    • Polyhedron
      • Tetrahedron
      • Hexahedron
      • Parallelepiped
      • Cuboid
      • Cube
    • Ellipsoids & balls
    • Trunk
      • Cylinder
      • Prism
      • Cone
      • Pyramid
      • RevTrunk
      • RevCylinder
      • RevCone
  • Mesh generation
    • Mesh generators
    • Transformations and extrusions
    • Mesh tools
    • Geometric element
  • Geometric domains
  • Approximation spaces and unknowns
    • Approximation spaces
    • Unknowns and test functions
    • Finite elements
  • Problem definition
    • Integration methods
    • Operators on unknowns/kernels
    • H-matrices
  • Algebraic representation
    • Matrix storages
    • TermMatrix and TermVector in details
  • Solvers
    • Iterative Solvers
    • Eigenvalue solvers
  • Third-party dependencies
    • Multi-threading with OpenMP
    • Using Arpack
    • Using Umfpack
  • Language reference
  • Approximation spaces and unknowns

Approximation spaces and unknowns#

The end user class to define approximation spaces is Space, essentially containing a pointer to the true approximation space object (child class of Space):

  • Finite element (sub)spaces (FeSpace and FeSubSpace)

  • Spectral spaces (SpSpace)

Contents:

  • Approximation spaces
    • The Space and SpaceInfo classes
    • The FeSpace class
    • The SpSpace class
    • The SubSpace and FeSubSpace classes
    • The ProdSpace class
    • The Spaces class
  • Unknowns and test functions
    • The Unknown class
    • The ComponentOfUnknown class
    • The Unknowns class
  • Finite elements
    • Available finite elements
    • The RefElement class
    • The Interpolation class
    • The GeomRefElement class
    • The RefDof class
    • The ShapeValues class
    • Bibliography

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Geometric domains

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Approximation spaces

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