Efficient Solution Techniques for a Finite Element Thin Plate Spline Formulation

We present a new technique for solving the saddle point problem arising from a finite element based thin plate spline formulation. The solver uses the Sherman–Morrison–Woodbury formula to divide the domain into different regions depending on the properties of the data projection matrix. We analyse the conditioning of the resulting system on certain data distributions and use the results to develop effective preconditioners. We show our approach is efficient for a wide range of parameters by testing it on a number of different examples. Numerical results are given in one, two and three dimensions.