Journal of Scientific Computing

, Volume 63, Issue 2, pp 374–409 | Cite as

Efficient Solution Techniques for a Finite Element Thin Plate Spline Formulation

  • Linda Stals


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.


Mixed finite elements Thin plate splines Saddle point problems Conditioning of matrices 

Mathematics Subject Classification

65M55 15A06 15A12 65D07 65D10 



The authour would like to thank the anonymous referees for their valuable comments. The time and care they have taken in reviewing the paper is much appreciated.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia

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