I have extracted the equations we need to implement from Stuart's paper:
Mesh-free data transfer algorithms for partitioned multiphysics problems: Conservation, accuracy, and parallelism. The equations are in the following file: spline.pdf
Note there were some tricks to get this to scale for the off-diagonal blocks. Also you could apply some of the scaling you guys did in moving least squares which should make the linear solve better condition.
I have extracted the equations we need to implement from Stuart's paper:
Mesh-free data transfer algorithms for partitioned multiphysics problems: Conservation, accuracy, and parallelism
. The equations are in the following file: spline.pdf