InterpolationElement(elements::X, constructNodes::Bool = true)

Initalize an interpolation element from a collection of tuple of simple elements. The optional second argument constructNodes determines whether or not predefined nodes should be used.

LineElement

Basic struct holding orthogonal polynomials on the line.

LineElement(n, geometry, params)

Construct interpolation object on a line with order n, some geometry and parameters params.

generateRanges(dimTuple)

Returns a Tuple of ranges which span 1:sum(dimTuple) with the property length(res[i]) == dimTuple[i]. Used to associate dimensions with rows in matrices.

generateTensorNodes!(res, tuple_nodes)

Generates a tensor product of input nodes tuple_nodes. The input is a tuple of node matrices. Columns of the node input store coordinates and rows store different nodes. The output is written into res. If the input nodes x_i have dimensions size(d_i, n_i) the output size(res) = (sum(d_i), prod(n_i)). The nodes are iterated first to last, i.e. ([e1_1 e1_2], [e2_1 e2_2]) -> [[e1_1, e2_1] [e1_2, e2_1] [e1_1, e2_2] [e1_2, e2_2]]

generateTensorNodes(tuple_nodes)

Allocating version of generateTensorNodes!

generateTensorNodes(tuple_nodes)

Allocating version of generateTensorNodes!

initalizeRecurrence!(buffer, x)

Triggers a reset of the buffer and sets the spatial variable of the buffer to x.

jacobiRecurrenceRelation(Pₙ₋₁, Pₙ₋₂, n, α, β, x)

Classical three terms recurrence relation for Jacobi-Polynomials defined on $(-1,1)$. Requires the two pervious terms Pₙ₋₁, Pₙ₋₂, the order n, the parameters α>-1, β>-1 and the location x as input. The value of the previous terms is irrelevant for n=0 and n=1.

setVandermonde(intElement::InterpolationElement{T,D,X,Y}, nodes::NTuple{D, AbstractMatrix{T}})

Update the Vandermonde matrix of an interpolation element for set of nodes.

updateInterpolation!(intElement::InterpolationElement, node_values::AbstractVector)

Update the modes of the interpolation from a function values. The structure of the node values fᵢ=f(xᵢ) must be the same as the one used for the xᵢ when initalizing the Vandermonde matrix.