[Colloquium] Talk by Tatyana Vdovina on Wed. October 4, 2006

[Margery Ishmael]

DEPARTMENT OF COMPUTER SCIENCE - TALK

Date: Wednesday, October 4, 2006
Time: 2:30 p.m.
Place: Ryerson 251

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Speaker: TATYANA VDOVINA

From:  University of Maryland, Baltimore County
Department of Mathematics and Statistics

Title:  Operator Upscaling for the Wave Equation

Abstract:

Wave propagation in  heterogeneous media results in models involving  
multiple scales.
Operator upscaling solves the problem on a coarse grid, but still  
retains subgrid
information and fine-scale input data. The method applied to the  
constant density,
variable sound velocity acoustic wave equation consists of two  
stages.  First,
the problem is solved for the subgrid component defined locally  
within each coarse
block. Then, the subgrid  solutions are used to augment the coarse- 
grid problem.
Due to the homogeneous Neumann boundary conditions imposed on each  
coarse block,
the subgrid problems decouple, which leads to the efficient parallel  
algorithm.
Two variable velocity numerical experiments illustrate that operator  
upscaling
captures the essential fine-scale information. We develop convergence  
analysis for
the method using energy techniques.  We show that in the H^1 norm the  
upscaled
solution converges linearly on the coarse scale, and pressure (which  
is not upscaled
in this implementation) converges linearly on the fine scale if  
Raviart-Thomas zero
spaces are used on both scales. The fully discrete scheme is also  
shown to be
second-order in time. We also discuss the application of operator  
upscaling
to the three-dimensional elastic wave equation.

***The talk will be followed by refreshments in Ryerson 255***

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Host:  Todd Dupont

People in need of assistance should call 773-834-8977 in advance.

For information on future CS talks: http://www.cs.uchicago.edu/events


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