I want to use convolution in CF，but I cannot find function that computing convolution in documentation
depends on …
How do you want to realize the convolution operators on unstructured grids on bounded domains ? do you have references ?
Hi Joachim,
In terms of numerical implementation, I have not found any reference materials. Currently, I am reading a paper on shape optimization. In the paper, a Gaussian convolution kernel is used to perform a convolution operation on the characteristic function of a set (∫𝐺𝑡(𝑥−𝑦)𝑋(𝑦)𝑑𝑦). I would like to inquire if there is a built-in convolution function in ngsolve. If not, I am considering writing one myself.
Best,
Yuanda Ye
Dear NGSolve team,
I am picking up this thread again because I have a similar query.
I would like to implement a weak form, which contains a convolution term in one spatial direction, and an usual integral in the other, in 2D slab geometry using curl-conforming quadrilateral basis functions.
To be specific, I am interested in electromagnetics such that I would have a curl-curl term, a vacuum term, a driving antenna term and “a non-local” plasma dielectric tensor \mathbf{K}(x,|y-y'|), the latter expressed as
\displaystyle \int \mathbf{F}^{*} \left ( x, y' \right ) \cdot \mathbf{K} \left ( x, | y-y' | \right ) \cdot \mathbf{E} \left ( x, y \right ) dx dy dy'
The direction of the convolution corresponds to the direction of a background magnetic field, taken exclusively in the y-direction. The test and trial functions \mathbf{F} and \mathbf{E} are evaluated at different locations along y (and do not belong to adjacent elements anymore).
It is my hope that applying a suitable transformation to a field-aligned system for a more general background magnetic fied would still reduce to the former equation modulo extra Jacobians.
Could you tell me if this is feasible and if there are ways to implement the convolution term? Either directly or using mylittle ngsolve?
Thank you very much in advance,
Yours sincerely
Bernard Reman
no, such operation is not allowed - since it does not fit into a finite element framework
Joachim