SELF_Lagrange Module

The number of target points.

The number of control points.

The boundary interpolation matrix that is used to map a grid of nodal values at the control points to the element boundaries.

The barycentric weights that are calculated from the controlPoints and used for interpolation.

A handle for working with hipblas

The set of nodes in one dimension where data is known. To create higher dimension interpolation and differentiation operators, structured grids in two and three dimensions are created by tensor products of the controlPoints. This design decision implies that all spectral element methods supported by the Lagrange class have the same polynomial degree in each computational/spatial dimension. In practice, the controlPoints are the Legendre-Gauss, Legendre-Gauss-Lobatto, Legendre-Gauss-Radau, Chebyshev-Gauss, Chebyshev-Gauss-Lobatto, or Chebyshev-Gauss-Radau quadrature points over the domain [-1,1] (computational space). The Init routine for this class restricts controlPoints to one of these quadrature types or uniform points on [-1,1].

The derivative matrix for mapping function nodal values to a nodal values of the derivative estimate. The dMatrix is based on a strong form of the derivative.

The derivative matrix for mapping function nodal values to a nodal values of the derivative estimate. The dgMatrix is based on a weak form of the derivative. It must be used with bMatrix to account for boundary contributions in the weak form.

The interpolation matrix (transpose) for mapping data from the control grid to the target grid.

The quadrature weights for discrete integration. The quadradture weights depend on the type of controlPoints provided; one of Legendre-Gauss, Legendre-Gauss-Lobatto, Legendre-Gauss-Radau, Chebyshev-Gauss, Chebyshev-Gauss-Lobatto, Chebyshev-Gauss Radau, or Uniform. If Uniform, the quadrature weights are constant $$dx = \frac{2.0}{N+1}$$ .

The set of nodes in one dimension where data is to be interpolated to. To create higher dimension interpolation and differentiation operators, structured grids in two and three dimensions are created by tensor products of the targetPoints. In practice, the targetPoints are set to a uniformly distributed set of points between [-1,1] (computational space) to allow for interpolation from unevenly spaced quadrature points to a plotting grid.