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SpECTRE
2021.08.02
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A cached exponential filter. More...
#include <ExponentialFilter.hpp>
Classes | |
| struct | Alpha |
The value of exp(-alpha) is what the highest modal coefficient is rescaled by. More... | |
| struct | DisableForDebugging |
| Turn the filter off. More... | |
| struct | HalfPower |
| Half of the exponent in the exponential. More... | |
Public Types | |
| using | options = tmpl::list< Alpha, HalfPower, DisableForDebugging > |
Public Member Functions | |
| Exponential (double alpha, unsigned half_power, bool disable_for_debugging) noexcept | |
| const Matrix & | filter_matrix (const Mesh< 1 > &mesh) const noexcept |
| A cached matrix used to apply the filter to the given mesh. | |
| bool | disable_for_debugging () const noexcept |
| void | pup (PUP::er &p) noexcept |
Static Public Member Functions | |
| static std::string | name () noexcept |
Static Public Attributes | |
| static constexpr Options::String | help = {"An exponential filter."} |
Friends | |
| template<size_t LocalFilterIndex> | |
| bool | operator== (const Exponential< LocalFilterIndex > &lhs, const Exponential< LocalFilterIndex > &rhs) noexcept |
A cached exponential filter.
Applies an exponential filter in each logical direction to each component of the tensors TagsToFilter. The exponential filter rescales the 1d modal coefficients \(c_i\) as:
\begin{align*} c_i\to c_i \exp\left[-\alpha_{\mathrm{ef}} \left(\frac{i}{N}\right)^{2\beta_{\mathrm{ef}}}\right] \end{align*}
where \(N\) is the basis degree (number of grid points per element per dimension minus one), \(\alpha_{\mathrm{ef}}\) determines how much the coefficients are rescaled, and \(\beta_{\mathrm{ef}}\) (given by the HalfPower option) determines how aggressive/broad the filter is (lower values means filtering more coefficients). Setting \(\alpha_{\mathrm{ef}}=36\) results in effectively zeroing the highest coefficient (in practice it gets rescaled by machine epsilon). The same \(\alpha_{\mathrm{ef}}\) and \(\beta_{\mathrm{ef}}\) are used in each logical direction. For a discussion of filtering see section 5.3 of [58].
size_t template parameter is to allow for different Alpha and HalfPower parameters for different tensors while still being able to cache the matrices. If different Alpha or HalfPower parameters are desired for filtering different tensors, then multiple filters must be inserted into the GlobalCache with different FilterIndex values. In the input file these will be specified as ExpFilterFILTER_INDEX, e.g.