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Optimization-based Conservative Transport on the Sphere

Presented by: 
Kara Peterson Sandia National Laboratories
Date: 
Tuesday 25th September 2012 - 10:15 to 10:40
Venue: 
INI Seminar Room 1
Session Title: 
Advection Session
Abstract: 
We present a new optimization-based conservative transport algorithm for scalar quantities (i.e. mass) that preserves monotonicity without the use of flux limiters. The method is formulated as a singly linearly constrained quadratic program with simple bounds where the net mass updates to the cell are the optimization variables. The objective is to minimize the discrepancy between a target or high-order mass update and a mass update that satisfies physical bounds. In this way, we separate accuracy considerations, handled by the objective functional from the enforcement of physical bounds, handled by the contraints. With this structure mass conservation is incorporated as a constraint and a simple, efficient, and easily parallelizable optimization algorithm is obtained. This algorithm has been extended to a latitude-longitude grid for two-dimensional remapping and transport on the sphere. Results for several standard test problems on the sphere will be shown to illustrate the accuracy and robustness of the method.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons