Matrices for filtering spectral coefficients. More...
Functions  
Matrix  exponential_filter (const Mesh< 1 > &mesh, double alpha, unsigned half_power) noexcept 
Returns a Matrix by which to multiply the nodal coefficients to apply a stable exponential filter. More...  
Matrices for filtering spectral coefficients.

noexcept 
Returns a Matrix
by which to multiply the nodal coefficients to apply a stable exponential filter.
The exponential filter rescales the modal coefficients according to:
\begin{align*} c_i\to c_i \exp\left[\alpha \left(\frac{i}{N}\right)^{2m}\right] \end{align*}
where \(c_i\) are the zeroindexed modal coefficients, \(N\) is the basis order, \(\alpha\) determines how much the coefficients are rescaled, and \(m\) determines how aggressive/broad the filter is (lower values means filtering more coefficients). Setting \(\alpha=36\) results in setting the highest coefficient to machine precision, effectively zeroing it out.