Department of Mathematics & Center for Computation and Technology LSU
Multi-scale analysis and optimal local basis functions for
Generalized Finite Element Methods
September 15, 2010
3:00pm SEC 204
Abstract
Modern structures such as airplane wings exhibit complicated sub structures
and make use of composite materials in their construction. The high cost of
experimental tests for these hierarchical structures is driving a trend
toward virtual testing. This requires the development of multi-scale
numerical methods capable of handling large degrees of freedom spread
across different length scales. In this talk we review multi-scale
numerical methods and introduce the theory of the Kolmogorov n-width as a
means to identify optimal local basis functions for use in multi-scale
finite element methods. We are able to identify a spectral basis with
nearly exponential convergence with respect to the dimension of the
approximation space. The convergence result is shown to hold in a very
general setting. This is joint work with Ivo Babuska.
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Last modified: April 11 2016 - 18:14:43