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  • Home
  • Examples
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  • Installation
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  • API
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  • Index
  • GitLab
  • POEMS
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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
  • Maths resources

Maths resources#

The mathResources library collects all the stuff related to mathematics tools such as polynomial roots, random generators, integration methods, ODE solvers, spline approximations, special functions, Green’s kernels and some exact solutions of PDE. Most of these are autonomous tools but may be used in the context of XLiFE++.

  • Polynomials and random generators
    • Polynomial roots
    • Random generators
  • Integration and ODE
    • Integral calculation tools
    • ODE solvers
  • Special functions and Green’s kernels
    • Special functions
    • Available Green’s kernels
    • User kernels
    • PDE exact solutions
  • Splines
    • C2 spline
    • Catmull-Rom spline
    • Bézier curve
    • B-Spline
    • Spline surfaces (nurbs)
  • Parametrizations
    • Piecewise parametrization
  • Geometrical transformations
    • Canonical transformations
    • General linear transformations
    • Composition of transformations
    • Applying transformations

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Keys for visualization

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Polynomials and random generators

© Copyright 2011-2026, Éric Lunéville, Nicolas Kielbasiewicz and the XLiFE++ Development Team.

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