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{\large Pavel Bochev \\
{\bf Better solvers through optimization, or how to avoid doing the hard work yourself}}

Sandia National Laboratories \\ P O Box 5800 \\ MS 1320 \\ Albuquerque \\ NM 87185-1320
\\
{\tt pbboche@sandia.gov}\\
Denis Ridzal\end{center}

In this talk we show how optimization and control ideas can be used to
obtain robust solvers and better methods for the numerical solution of
mathematical models comprising of PDEs with fundamentally different
mathematical properties. We will present an additive decomposition
approach for coupled multi-physics problems which uses optimization
formalism to expose the constituent component physics operators. In this
setting, our optimization-based approach allows to synthesize a robust
and efficient solver for the coupled problem from simpler solvers for the
component physics equations. To illustrate the scope of the approach we
show how a scalable solver for a scalar advection-dominated PDE can be
derived from a standard, off-the-shelf algebraic multigrid for the
Poisson equation, that does not work for this equation.


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