Mohamed Sulman (WPI) - Higher Dimensional Adaptive Grid Methods Based on Solving the Monge-Kantorovich Problem
Mathematics - Colloquium
| Date & Time: |
Thursday, December 3, 2009 4:00 PM-5:00 PM |
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| Suggested Audiences: | Adult, College | |
| Location: Find Local Food & Accommodations |
WPI: Stratton Hall 202 100 Institute Road Worcester, MA 01609-2280 |
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| Description: | ABSTRACT: The use of adaptive grid methods is fundamental to the numerical solution of differential equations that involve large solution variations. These methods seek to provide efficient numerical solutions with high accuracy. In this talk, I will describe a newly developed approach for adaptive gird generation in higher dimensions based on solving the optimal mass transportation problem also known as the L^2 Monge–Kantorovich problem (MKP). The coordinate transformation used to define the grid adaptation is determined using two different methods. In the first method, the transformation is computed by solving a parabolic Monge-Amp`ere equation for a steady state solution. For the second method, the grid movement is determined from the velocity field obtained by solving the fluid dynamics formulation of the L^2 MKP. The experimental results show that the MKP methods show promise as effective and reliable methods for higher dimensional adaptive grid generation. | |
| More Information: |
E-mail:
ma-chair@wpi.edu
Entered by: WPI: Mathematical Sciences Department |
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Created: November 10, 2009 at 4:13 PM
Last Modified: November 23, 2009 at 10:25 AM
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