NodesAndModes.Pyr

abctorst(a,b,c)

Converts from Stroud coordinates (a,b,c) on [-1,1]^3 to reference element coordinates (r,s,t).

basis(N,r,s,t,tol=1e-12)

Computes orthonormal semi-nodal basis on the biunit pyramid element.

Warning: nodal derivative matrices may contain errors for nodes at t = 1. A way to avoid this is to use weak differentiation matrices computed using quadrature rules with only interior nodes.

equi_nodes(N)

Computes equispaced nodes of degree N.

grad_vandermonde(N,r)

Computes the generalized Vandermonde derivative matrix V of degree N at points r. Specialized for the 1D case

grad_vandermonde(N,rst...)

Computes the generalized Vandermonde derivative matrix V of degree N at points (r,s,t).

nodes(N)

Computes interpolation nodes of degree N. Edge nodes coincide with (N+1)-point Lobatto points. Triangular face nodes coincide with Tri.nodes(N), quadrilateral face nodes coincide with tensor product (N+1)-point Lobatto points.

quad_nodes(N)

Computes quadrature nodes and weights which are exact for degree 2N polynomials.

stroud_quad_nodes(N)

Returns Stroud-type quadrature nodes constructed from the tensor product of (N+1)-point Gauss-Jacobi rules. Exact for degree 2N polynomials

vandermonde(N,r)

Computes the generalized Vandermonde matrix V of degree N at point r. Specialized for the 1D case

vandermonde(N,rst...)

Computes the generalized Vandermonde matrix V of degree N at points (r,s,t).