[8-13]Multi-level Domain Decomposition Preconditioners and Applications in Solving Inverse Elliptic Problems

Date:2009-08-10

Title：Multi-level Domain Decomposition Preconditioners and Applications in Solving Inverse Elliptic Problems
Speaker：Si Liu
Time：11:00-11:40 am, Thursday, August 13
Venue：Room 334, Level 3 Building #5

Abstract：

Inverse problems are typically ill-posed and difficult to solve, and solving them usually leads to the establishment of optimization problems. However, these optimization problems need to be reformulated for numerical treatment, such as adding assumptions or restrictions for the function space. In our research, we focus on the parameter identification problems. Specifically, we aim at computing the diffusion coefficients in elliptic partial differential equations. A number of significant applications include determination of the transmissivity for the groundwater system, recovery of the Lame parameter in elastic materials, etc.
We have developed a fully coupled Lagrange-Newton-Krylov-Schwarz (LNKSz) algorithm and software for solving these inverse elliptic problems. In particular, we have developed a series of two-level domain decomposition techniques that introduce a coarse grid operator into the single level domain decomposition method, as the preconditioner in the Jacobian system. We have also studied several different strategies for solving the subdomain and coarse-level problems. We report the performance of our algorithms in terms of the number of linear and nonlinear iterations, their sensitivity with respect to the level of noise in the data, the total computing time, and parallel scalability on a super computer with up to 1024 processors.

Biography：
Si Liu graduated from Peking University with a BS degree in 2004 and received his Master’s degree in Applied Mathematics at the University of Colorado in 2006. He is currently pursuing a PhD degree under Prof. Xiao-Chuan Cai in the University of Colorado. His research interests include inverse problems, high performance computing, domain decomposition and multigrid methods.