How do I change nodal coordinates in a 2D mesh without changing anything else?

Question

I have a 2D mesh that I generated via ToElementMesh. It discretizes a square domain with a small hole whose shape comes from a parametric B-spline. I now want to change the shape of the hole very very slightly and produce a new mesh identical in every respect to the original, except that (only) the coordinates of nodes on the hole are changed. The change is small enough so that I do not have to worry about excessive element distortion. Is there any way to update "Coordinates" in the mesh "object" without changing anything else in it?

I tried to build the new mesh manually by extracting "Coordinates" and "MeshElements" from the original. For instance,

XC = meshoriginal["Coordinates"];
ME = meshoriginal["MeshElements"];
meshupdated = ToElementMesh["Coordinates" -> XC, "MeshElements" -> ME];

changes many properties in meshupdated, which I want to keep the same as in meshoriginal (e.g., "BoundaryElements" and several other properties change);

The purpose of this is to compute a finite difference estimate of the gradient of the response with respect to the B-spline parameters.

I apologize in advance if my question does not conform to this forum standards. It's the first time I ask a question. Thanks!

Answer 1

You can use

newcoords = updatecoords[XC];
meshupdated = ToElementMesh["Coordinates" -> newcoords, "MeshElements" -> ME,
                            "BoundaryElements" -> meshoriginal["BoundaryElements"],
                            "PointElements" -> meshoriginal["PointElements"]];

That can be sped up (if you are absolutely sure the structure of the mesh did not change) by giving options changing the options of ElementMesh:

Options[ElementMesh]
{"CheckIncidentsCompletness" -> True, 
 "CheckIntersections" -> Automatic, "CheckQuality" -> Automatic, 
 "DeleteDuplicateCoordinates" -> True, "MessageHead" -> Automatic}

to

opts = {"CheckIncidentsCompletness" -> False, "CheckIntersections" -> False, 
        "CheckQuality" -> Automatic, "DeleteDuplicateCoordinates" -> False, 
        "MessageHead" -> Automatic}

and give that to ToElementMesh[...., opts]