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Date: Mon, 27 Oct 1997 01:22:19 -0700 (MST)
From: Marian Brezina <mbrezina@tiger.cudenver.edu>
Subject: abstract.tex
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Dear Craig, 
here is the page with the title and abstract. 

Cheers
Marian 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentstyle[12pt]{article} 
\begin{document}
\pagestyle{empty}
\author{Marian Brezina}
\title{Robust Iterative Methods on Unstructured Meshes}
\date{1997} 
\maketitle 
\begin{abstract}
   We propose and analyze three multilevel iterative solvers 
   of both domain decomposition and multigrid type.  
   All of these methods are algebraic, allowing almost or fully black-box 
   implementation. Their development was motivated by the need to solve 
   large algebraic systems of equations resulting from finite element 
   discretizations of self-adjoint, second order 
   uniformly elliptic problems on unstructured three-dimensional meshes. 
   Two of the methods discussed perform a simple, but effective 
   domain decomposition as a part of the solving process. 
   This allows for a remarkable adaptivity, where the decomposition is 
   generated depending on the difficulty of the problem without requiring 
   an input of a different decomposition.    
   We focus on achieving robustness features that allow 
   using the new methods as a replacement of direct solvers for solving these 
   systems.   The new methods are superior in terms of computational 
   complexity and storage requirements.  
   On serial architectures, the asymptotic computational complexity 
   of these methods for solving 3D problems is shown to  
   be in the range of $O(n^{7/6})$ and $O(n^{49/33})$.   
   The methods all benefit from implementation on modern parallel architectures
   which can reduce the computational complexity to $O(n^{7/6})$ for all three 
   methods.
   The theoretical results are accompanied by computational experiments
   confirming the theoretically predicted convergence properties
   and suggesting the potential of the methods for solving a wider 
   variety of problems than those % the ones 
   covered by the current theory.  
\end{abstract}
\end{document}