Mesh Refinement Routines

johannes_s · January 23, 2023, 1:34pm

Hello.

i) Which refinement routine is used for local (adaptive) mesh refinements? I haven’t found anything in the documentation.

ii) Is there a simple way to include an alternative routine like the one of Maubach in “Local Bisection Refinement for N-Simplicial Grids Generated by Reflection”?

iii) Are there already different refinement routines included?

Kind regards,
Johannes

hvwahl · February 3, 2023, 10:24am

Hi Johannes,

regarding (i), the doc-string of the Mesh class states

| Refine(…)
| Refine(self: ngsolve.comp.Mesh, mark_surface_elements: bool = False, onlyonce: bool = False) → None
|
| Local mesh refinement based on marked elements, uses element-bisection algorithm

regarding (iii) In the Navier-Stokes workshop materials from the third NGSolve User Meeting, there is a script wich implements barycentric mesh refinement in python. This may be a good starting point to implement your own mesh refinement routine.

Best wishes
Henry

johannes_s · February 7, 2023, 8:02am

Hi, thanks for your answer. Is the bisection routine somewhere specified, that is, does the program use longest-edge bisection or the bisection routine of Maubach/Traxler?

Kind regards,
Johannes

smyrback · April 9, 2024, 12:42pm

Hi, can I access the code mentioned in point (iii) somehow? The website for the code material from NGSolve user meeting 3 is not working. I would love to see how one can implement a barycentric mesh refinement.

joachim · April 10, 2024, 2:59am

Hi,
the bisection is based on
Douglas N. Arnold, Arup Mukherjee, and Luc Pouly. Locally adapted tetrahedral meshes using bisection . SIAM J. Sci. Comput. , 22(2):431-448, 2000

You can have a look into the code here:

github.com

NGSolve/netgen/blob/master/libsrc/meshing/bisect.cpp

#include <mystdlib.h>
#include <core/array.hpp>
#include "bisect.hpp"
#include "validate.hpp"

#define noDEBUG


namespace netgen
{
  class MarkedTet
  {
  public:
    /// pnums of tet
    PointIndex pnums[4];
    /// material number
    int matindex;
    /// element marked for refinement
    /// marked = 1: marked by element marker, marked = 2 due to closure
    unsigned int marked:2;

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Joachim

smyrback · April 10, 2024, 6:54am

I see. I am interested in the barycentric refinement, also sometimes called Clough-Tocher split (used in e.g. “A CutFEM Divergence-Free Discretization for the Stokes Problem” by Haoran Liu, Michael Neilan, and Maxim Olshanskii.

Do you have it?

joachim · April 10, 2024, 4:00pm

see cell [10] here:
https://docu.ngsolve.org/latest/i-tutorials/unit-2.6-stokes/stokes.html

and some more using PETSc DMPlex:
https://ngspetsc.readthedocs.io/en/latest/notebooks/Meshes.html

Joachim