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Journal of Scientific Computing

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01-05-2015

Efficient Solution Techniques for a Finite Element Thin Plate Spline Formulation

Author: Linda Stals

Published in: Journal of Scientific Computing | Issue 2/2015

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Abstract

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.

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Title: Efficient Solution Techniques for a Finite Element Thin Plate Spline Formulation
Author: Linda Stals
Publication date: 01-05-2015
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 2/2015
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-014-9898-x

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