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{\large Si Liu \\
{\bf Multilevel Domain Decomposition Algorithms for Inverse Elliptic Problems }}

2300 Arapahoe Ave \\ Apt 324 \\ Boulder \\ CO 80302
\\
{\tt sliu@colorado.edu}\\
Xiao-Chuan Cai\\
{\em Department of Computer Science, University of Colorado at Boulder}\end{center}

We investigate scalable multilevel domain decomposition algorithms for
solving inverse elliptic problems formulated as optimization problems
constrained by partial differential equations. To solve these
optimization problems, we employ a fully coupled
Lagrange-Newton-Krylov-Schwarz algorithm. One of the key steps in the
algorithm is the Jacobian preconditioning, for which we study and compare
four types of two-level
domain decomposition methods. Our numerical results show that the
algorithms work well for different types of observations in terms of the
accuracy of the solution, and some of the algorithms scale better than
the others when the number of processors is large. We also study and
report the sensitivity
of the algorithms with respect to the jumps of the coefficients, the
level of noise in the observed data, the size of the computational
domain, the size of the mesh, and the number of processors.


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