I am a solving a problem using symmetric interior penalty discontinuous Galerkin and I am running into convergence issues that I am attributing to labeling of internal facets.
I need to impose a flux expression on the internal boundary between the pink and the turquoise colored subdomains.
The expression for flux that I need to impose is: -\kappa \nabla u \cdot n_{\mathrm{turquoise}} = \gamma (u_{\mathrm{turquoise}} - u_{\mathrm{pink}} - \mathrm{constant})
I obtain convergence when the boundary between the pink and turquoise domains is a straight line.
My solution involves replacing the jump of u
[\![ u ]\!] in the internal facet integral with (\mathrm{constant} - \frac{\kappa}{\gamma}\nabla u \cdot n_{\mathrm{turquoise}})n_{\mathrm{turqoise}} .
In such a boundary, is there a way to know which is the subdomain that provides u(``+") and n(``+"), and which subdomain provides u(``-") and n(``-")?
Further investigation shows that it is related to Facets orientation in inner surface with fenicsX - #3 by RaphaelC, but I cannot figure out what the solution is. At the interface between the subdomains, the orientation needs to be definite. For example, I may want the turquoise domain to be “+” and the pink domain to be “-”.
Given now that I have control over direction of ordering, how do I express a function such as ufl.sqrt([\![ u ]\!]) where [\![ u ]\!] is a jump that is non-zero? I am unclear how to combine the labeling that I have made according to Add one-sided integration example as example of custom integration · Issue #158 · jorgensd/dolfinx-tutorial · GitHub to generate a function that takes the square root of the local jump and integrates once over the shared interface.
Nothing wrong with that. I am trying to figure that out from the ufl library, but it’s a slow process and any tips you provide is greatly appreciated. What I need is for “+” side to be on the side of domain with higher cell tag and “-” to be on the side of domain with lower cell tag if the facet is an internal boundary shared by two subdomains. For facets not at the internal boundary between two subdomains, I can use default behavior of “+” and “-” sides.
I wouldn’t necessarily rely on us resurrecting a fix that was dismissed years ago. OK, so since indeed you can’t rely on + and -, can’t you expand the definition of jump, use its linearity, and write the two integrals separately?
In the integral tuple we create with integration entities, (cell_0, local_ facet_index_ cell_0, cell_1, local_facet_index_cell_1) the plus restriction is the first cell (0), while the negative restriction is cell 1. thus by manually packing them in that order you can get a directional jump
Marking only 1 internal boundary where I want deterministic “+” and “-” sides is sufficient for my current problem, but it’d be great to learn if it possible (if so how) to label multiple internal boundaries for deterministic “+” and “-” sides.
I appreciate both of you for your help and patience.
My specific usage required me to reorder facets at only one boundary and it was not necessary to add more than one tag to dS. Poisson submesh DG coupling · GitHub has some utility functions that you may find helpful.
