[Talks] Brown CS Thesis Defense: Vasiliki Chatzi talk in Lubrano on 5/12/2000 at 11:00 AM

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			  CS Thesis Defense
		  The Department of Computer Science
			   BROWN UNIVERSITY

			       presents

			   Vasiliki Chatzi
			    

		   Friday, May 12, 2000 at 11:00 AM

	       Lubrano Conference Room (CIT 4th floor)

		  

	      ``Integer-Coordinate Crystalline Meshes''

			       
			       Abstract


The finite-element method is one of the tools commonly used today to
approximately solve partial differential equations associated with a
physical region. The first step of the method consists of constructing
the {\em finite element mesh}.  The mesh affects not only how accurate
our solution is but also how fast it can be computed.

We present {\em integer-coordinate crystalline meshes} which were
designed to combine the advantages of both structured and unstructured
meshes. A mesh is called {\em crystalline} if it consists of regular
elements whose vertices are positioned on a regular grid.  Our
crystalline meshes are conformal, allow us to use elements of
different sizes in different regions of the domain and use a small
number of distinct element shapes.  This allows for accurate and fast
computation.  To minimize numerical errors, we require that all
element vertices are placed on integer coordinates.  This guarantees
that point placement can always be done accurately.

We will describe how crystalline meshes can be obtained from a
description of the domain. It turns out that the most challenging part
is finding a good approximation of the boundaries. We will give
mechanisms that can be used to find such a good approximation. We will
also present a method that can be used to construct basis functions
for pyramidal finite elements of order $k$, for any $k> 0$.



  
		     Host: Professor Franco Preparata