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Section Navigation

  • XLiFE++’s basics
    • Basic types
    • Vectors and matrices
    • Functions and kernels
    • The Parametrization class
    • 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
    • Splines
    • Special functions and Green’s kernels
  • Mesh generation
    • 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 generators
    • Transformations and extrusions
    • 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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