I have a dataset with discontinuous displacements across a few surfaces (so far I am working in 2D, so these would be lines, 1D). It is input as a PVDReader (just in case it makes any difference for the question, which I doubt).
Is there any way to programmatically create a new Source with the displacement jumps along those lines? Note that this new field would probably have to be defined on a domain with a lower dimension, see above.
So far, I created filters PlotOverLine, on lines slightly below and slightly above the prescribed line. But I do not know how to subtract the two and place them in a single field over the line.
Notes:
- So far I am working in 2D (domain where the discontinuity is defined is 1D). I mean to get also discontinuities in fields on 3D domains (domain where the discontinuity is defined is 2D).
- As a simple example (see below) I take for Domain of discontinuity: x axis, y=0. I actually mean to have an arbitrary line (in 2D) or plane (in 3D).
- I would provide an extra reward if the Domain of discontinuity is an arbitrary curve (in 2D) or surface (in 3D).
Mathematical description:
Discontinuous field: u(x,y)
Domain of discontinuity: x axis, y=0
Value of the field on one side of the domain of discontinuity: u(x+,0)
Value of the field on the other side of the domain of discontinuity: u(x-,0)
Jump in the field: d(x) = u(x+,0) - u(x-,0)
The field u is defined on a 2D domain. The field d is defined on a 1D domain (x axis).