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Contents : Additive Operator Decomposition and Optimization-Based Coupling with Applications. The Curious Case of Scalable AMG for Advection-Dominated PDEs Pavel Bochev Sandia National Laboratories Thursday May 14th 16:00 - 17:00 Room GUG 416 Abstract We develop and analyze an optimization-based approach for robust solution of PDE problems comprised of multiple physics operators with fundamentally di erent mathematical properties. Our approach relies on three essential steps: additive decomposition of the original problem into subproblems for which robust solution algorithms are available integration of the subproblems into an equivalent PDE-constrained optimization problem using distributed controls and solution of the resulting optimization problem. This strategy gives rise to a general approach for synthesizing robust solvers for complex coupled problems from solvers for their simpler physics components. We prove existence and uniqueness of solutions to the reformulated problem and establish regularization error estimate. An application to a scalar advection-di usion PDE illustrates the new approach. In particular we derive a robust iterative solver for advection-dominated problems using standard multilevel solvers for the Poisson equation. This is joint work with D. Ridzal. 1

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