4.7 Kernel

This directory contains two files, kernel.h and kernel.cpp, both of which are related to the line-SIAC (L-SIAC) filtering [2743] of FEM solutions. SIAC filtering takes the form:

        ∫       (     )
u*(x) =   ∞ K    ξ---x  u (ξ)dξ
         -∞   H    H     h

where uh denotes the FEM (continuous Galkerkin or discontinuous Galerkin) solution and KH represents a kernel function:

            M      (       )
         -1 ∑       -x
KH (x) = H     cγψ  H  - ζγ  .

In this expression, the functions ψ(x) are B-Splines. The two kernel files in this directory provide all the tools needed to construct the B-Spline functions and the kernel function described above.