Bishesh Khanal <[email protected]> writes: > Within A, for now, I can consider mu to be constant, although later if > possible it can be a variable even a tensor to describe anisotropy. But to > start with I want put this a constant. > The original equations start with mu (grad(u) + grad(u)^T) but then > simplifications occur due to div(u) = f2
Rework that step in case of variable mu. > I'm mostly interested in the phenomenon in A with my model, here B is the > extension of the very irregular domain of A to get a cuboid. Here, in B I > release the div(u) = f2 constraint and just put a regularisation to > penalize large deformation. What is of importance here is to compensate the > net volume expansion in domain A by corresponding contraction in domain B > so that the boundaries of the cuboid do not move. It does not particularly > represent any physics except probably that it gives me a velocity field > having a certain divergence field that penalizes big deformations. Okay, sounds like it's already an artificial equation, so you should be able to leave in a normal equation for p, with a big mass matrix on the diagonal, div(mu(grad(u))) - grad(p) = f1 div(u) - c(x) p = f2 c(x) = 0 in domain A and c(x) is large (the inverse of the second Lamé parameter) in domain B. > I do not know much about FEM. But some of the reasons why I have avoided it > in this particular problem are: (Please correct me on any of the following > points if they are wrong) > 1. The inputs f1 and f2 are 3D images (in average of size 200^3) that come > from other image processing pipeline; it's important that I constrain u at > each voxel for div(u) = f2 in domain A. I am trying to avoid having to get > the meshing from the 3D image(with very detailed structures), then go back > to the image from the obtained u again because I have to use the obtained u > to warp the image, transport other parameters again with u in the image > space and again obtain new f1 and f2 images. Then iterate this few times. Okay, there's nothing wrong with that.
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