On Wed, Nov 13, 2013 at 10:06 PM, Jed Brown <[email protected]> wrote:
> 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. > > Thanks, this looks quite reasonable. I'll try to experiment with it. > > 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. > Thanks for the confirmation.
