Hexahedral mesh creation and adjustment for modeling of a 3D printing process

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I'm looking for a way to create a hexahdral mesh for a geometry that will slightly change iteratively via Python. At the same time it will change significantly over more iterations. As mentioned in title it is for 3D printing, so it can be imagined. The thing is that it look inefficient to create mesh from scratch on each iteration and I'd like to just add new element and refine mesh near added region. As input I have initial STL model and G-code, determining path at which material will be added. I'm not very familiar with terms in mesh creation, so maybe it is the reason for not finding anything on this in documentation of different packages.

I looked through documentation of some packages like Gmsh, PyMesh, but haven't found information on such adaptive meshes. Although thought about implementation from scratch, but it looks like there is too much to look into for now.

So, I hope that if somebody knows about how to solve such problem, or how it called in professional field of meshing, for me to find information on it more effectively, you could share, thanks in advance)

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