The Mathematical Institute, University of Oxford, Eprints Archive

Calculus on surfaces with general closest point functions

März, T. and Macdonald, C. B. (2012) Calculus on surfaces with general closest point functions. SIAM Journal on Numerical Analysis . (Submitted)

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Abstract

The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a general class of these closest point functions (a subset of differentiable retractions), show that these are exactly the functions necessary to satisfy the above idea, and give a geometric characterization this class. Finally, we construct some closest point functions and demonstrate their effectiveness numerically on surface PDEs.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1495
Deposited By:Peter Hudston
Deposited On:02 Mar 2012 07:43
Last Modified:02 Mar 2012 07:43

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