SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Alignment of optimally transported meshes

C. Budd and E. Walsh

Abstract
Solutions of partial differential equations are often highly anisotropic and have strongly directional features. Examples include PDES which have shocks and interfaces in the solution. When calculating the solutions to these PDEs it is important to use computational meshes which align themselves with features in the solution. In this talk I will describe a mesh redistribution algorithm based on optimal transport methods which is cheap and robust to implement. I will show further (including giving a set of rigorous results) that this method is very effective at aligning elements along solution features including linear shocks and radially symmetric structures. This allows the solutions to be very well approximated and I will give results to prove this.

Organized by         Universidad de Valladolid     IMUVA