TriangleInterpolationUtility
This module contains some useful routines for polynomials approximations on the triangles.
Following methods are defined in this module.
- LagrangeDegree_Triangle Returns the monomial degrees of the Lagrange polynomials.
- LagrangeDOF_Triangle Returns the total number of degrees of freedom for a Lagrange polynomial.
- LagrangeInDOF_Triangle Returns the total number of degrees of freedom inside the triangle (cell degree of freedoms)
- EquidistanceInPoint_Triangle Returns the equidistance points which are strictly inside the triangle.
- EquidistancePoint_Triangle Returns the equidistance points on triangle, which can be used for constructing Lagrange polynomials.
- InterpolationPoint_Triangle Returns the interpolation points on the triangle. It can support various types of points on the triangle.
- LagrangeCoeff_Triangle Returns coefficients to form Lagrange polynomials.
- Dubiner_Triangle Returns the orthogonal basis on the triangle.
- BarycentricVertexBasis_Triangle Vertex basis in terms of Barycentric coordinates.
- BarycentricEdgeBasis_Triangle
- BarycentricHeirarchicalBasis_Triangle
- VertexBasis_Triangle
- EdgeBasis_Triangle
- CellBasis_Triangle
- HeirarchicalBasis_Triangle
- LagrangeEvalAll_Triangle
LagrangeGradientEvalAll_TriangleHeirarchicalBasisGradient_TriangleOrthogonalBasisGradient_TriangleQuadraturePoint_TriangleIJ2VEFC_TriangleFacetConnectivity_TriangleRefElemDomain_Triangle
Methods
📄️ LagrangeDegree_Triangle
Returns the polynomial space for constructing the Lagrange polynomials.
📄️ BarycentricEdgeBasis
Returns the edge basis functions on reference Triangle.
📄️ BarycentricHeirarchicalBasis
Evaluate all modal basis (Heirarchical polynomials) on Triangle.
📄️ BarycentricVertexBasis
Returns the vertex basis functions on reference Triangle.
📄️ CellBasis
Evaluate basis functions in the cell.
📄️ Dubiner_Triangle
Forms Dubiner basis on reference triangle domain. Reference triangle can be "biunit" or "unit".
📄️ EdgeBasis
Evaluate basis functions on left and right edge of biunit Triangle.
📄️ EquidistanceInPoint_Triangle
This function returns the equidistance points in triangle.
📄️ EquidistancePoint_Triangle
This function returns the nodal coordinates of higher order triangle element.
📄️ HeirarchicalBasis_Triangle
Evaluate all modal basis (heirarchical polynomial) on Triangle.
📄️ InterpolationPoint_Triangle
This routine returns the interpolation points on triangle.
📄️ LagrangeCoeff_Triangle
Returns the coefficients for Lagrange polynomial.
📄️ LagrangeDOF
Returns the total number of degree of freedom for a Lagrange polynomial on triangle.
📄️ LagrangeEvalAll
Evaluate Lagrange polynomials on triangle.
📄️ LagrangeInDOF
Returns the total number of degree of freedom for a lagrange polynomial in cell/face of triangle.
📄️ QuadraturePoint
This routine returns the quadrature points on triangle.
📄️ VertexBasis_Triangle
Returns value of vertex function on triangle.