InterpolatingBasis

This is an introduction to the InterpolatingBasis class. We write a small overarching summary of the class where we define the algorithm/equation/structure reasoning for having this class or where it fits with the rest of the code.

class InterpolatingBasis : public mrcpp::ScalingBasis

Interpolating scaling functions as defined by Alpert etal, J Comp Phys 182, 149-190 (2002).

Public Functions

inline InterpolatingBasis(int k)

Parameters:

k – [in] Polynomial order of basis, 1 < k < 40

Returns:

New InterpolatingBasis object

Private Functions

void initScalingBasis()

Initialise interpolating scaling basis.

Fills std::vector<Polynomial> funcs declared in the base class ScalingBasis with the interpolating scaling functions

\[ \varphi_j(x) = \sqrt{ w_j } \sum_{m = 0}^k \phi_m(x_j) \phi_m(x) , \quad x \in (0, 1) , \quad j = 0, \ldots, k , \]

where \( \phi_m \) are the Legendre scaling functions. Here \( k \) is order declared in the base class.

Note

These interpolating scaling functions are defined on the unit interval \( (0, 1) \).

void calcQuadratureValues()

In Progress by Evgueni…

void calcCVMaps()

In Progress by Evgueni…