Hello all,

I have a discrete 2nd order tensor field that I would like to interpolate to other points if possible.

To be more specific, I have a discrete two dimensional geometrical grid (x, y). To each point (x, y) in this 2-D geometry, is associated a material property that is a 2 x 2 matrix and that I have computed the value.

This material is intended to be used in a finite element simulation with the package COMSOL Multiphysics and obviously the location of the grid points where I computed the material properties will not correspond to the nodal points on the mesh for my finite element simulation.

I believe this leaves me with the change of finding a way to interpolate my tensor field before getting it into COMSOL. This is something not to hard to with scalar fields and COMSOL actually interface with Matlab to allow interpolation functions for scalar fields given discrete values. However, I have yet to encounter any situation where interpolating a tensor field was require.

Is there any scheme in Mathematica (I am somewhat new to Mathematica) that allows the interpolation of tensor fields?

Has anyone dealt with interpolation of tensor fields in mathematics in general?

Any other approach to accomplishing my goal (there may be guys in the field of electromagnetic cloaking that dealt with this situation)?

I am hoping not to have to first find nodal coordinates and then use Mathematica to generate a new grid of material properties at those coordinates and input it back into COMSOL; this would make mesh refinement a very tedious work....

Thanks,

Saliou Telly