Enable interpolation for shells using spherical harmonics #6479
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wthrowe
requested changes
Feb 14, 2025
| * | ||
| * \note The accuracy of the interpolation will depend upon the number and | ||
| * distribution of the source points. It is strongly suggested that you | ||
| * carefully investiage the accuracy for your use case. |
| namespace intrp { | ||
| /*! | ||
| * \brief Computes the matrix for interpolating a non-periodic function known at | ||
| * the set of points \f$x_{source}\f$ to the set of points \f$x_{target}\f$ |
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This is polynomial interpolation? Do you have a citation for the algorithm?
| * \details The returned matrix \f$M\f$ will have \f$n_{target}\f$ rows and | ||
| * \f$n_{source}\f$ columns so that \f$f_{target} = M f_{source}\f$ | ||
| * Formally, this computes the sum | ||
| * \f[ n w_j = 1 + 2 \sum_{k=1}{\lfloor (n-1)/2 \rfloor} \cos(k(x - X_j)) |
| * source_mesh. (These are equivalent to those returned by | ||
| * Spectral::interpolation_matrix.) | ||
| * - For a Fourier basis, the matrix is given by | ||
| * intrp::fourieer_interpolation_matrix at the quadrature points of the |
These will be used to construct interpolation matrices for basis functions other than Chebyshev and Legendre functions.
No longer store the coordinates in the class; just pass them in as function arguments.
This interpolator interpolates dimension by dimension and can handle spherical harmonic interpolation.
The interpolation matrix for the Irregular interpolant is used to interpolate in all dimensions at once. It is constructed by combining one-dimensional interpolation matrices. For spherical harmonics, these 1D matrices are provided by a Cardinal interpolator.
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Proposed changes
Adds ability to interpolate if the basis is spherical harmonic
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bugfixornew featureif appropriate.Further comments