März, T. and Macdonald, C. B. (2012) Calculus on surfaces with general closest point functions. SIAM Journal on Numerical Analysis . (Submitted)
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.
|Subjects:||D - G > General|
|Research Groups:||Oxford Centre for Collaborative Applied Mathematics|
|Deposited By:||Peter Hudston|
|Deposited On:||02 Mar 2012 07:43|
|Last Modified:||29 May 2015 19:11|
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