# Energy minimizing coarse spaces with functional constraints

## Prof. Ludmil Zikatanov

Dec. 14, 2010, 3:30 p.m. P 004

We will report on the construction of energy minimizing coarse spaces built
by patching solutions to appropriate saddle point problems. We first set an
abstract framework for such constructions, and then we give an example of
constructing coarse space and stable interpolation operator for the two level
Schwarz method.We apply the theoretical results in the design of coarse spaces
for discretizations of PDE with large varying coefficients. The stability and
approximation bounds of the constructed interpolant are in a weighted norm
and are independent of the variations in the coefficients. Such spaces can be
used in two level overlapping Schwarz algorithms for elliptic PDEs with large
coefficient jumps generally not resolved by a standard coarse grid. This is a
joint work with Robert Scheichl (University of Bath, UK) and Panayot S.
Vassilevski (Lawrence Livermore National Lab).