3D interpolation: From FVM to FEM nodes and back

vasilis

Hi,

I am doing fluid-structure interaction. There exists a code which solves the N.S eqns with FVM, and I am developing a code to deform the structure with FEM. At the interface I will transfer the stresses from the fluid to the solid mesh, and for that I need to interpolate from the FVM nodes to the FEM nodes. Initially, the domain is a cylinder.

I am thinking that the best way to achieve this is to find a function that goes through all the FVM nodes, and then use this function to calculate the value of the stress at the FEM nodes. For the moment I will consider the simplest form for the function, i.e. f(x,y,z)=Sum a(i,j,k) x^i y^j z^k, and this sum goes from 0 to 2 for i,j,k.

There are two thing that bother me: 1) The above function has 10 coefficients whose value will be determined by n points (n>10). I am thinking of the least square method for that. 2) Will this function be able to capture the abnormality of the surface?

Could someone suggest me a paper to read. I know that there is a lot of work on splines, and so I really need someone to direct me to the proper paper.

Thank you in advanced for your time