Analysis and PDE Seminar

Title:  Automating and Stabilizing the Discrete Empirical Interpolation Method for Nonlinear Model Reduction

Abstract:  The Discrete Empirical Interpolation Method (DEIM) is a technique for model reduction of nonlinear dynamical systems.  It is based upon a modification to proper orthogonal decomposition which is designed to reduce the computational complexity for evaluating reduced order nonlinear terms.  The DEIM approach is based upon an interpolatory projection and only requires evaluation of a few selected components of the original nonlinear term.  Thus, implementation of the reduced order nonlinear term requires a new code to be derived from the original code for evaluating the nonlinearity.  I will describe a methodology for automatically deriving a code for the reduced order nonlinearity directly from the original nonlinear code.  Although DEIM has been effective on some very difficult problems, it can under certain conditions introduce instabilities in the reduced model.  I will present a problem that has proved helpful in developing a method for stabilizing DEIM reduced models.

Date:
-
Location:
745 Patterson Office Tower

Analysis and PDE Seminar

Title:  Lp norms of eigenfunctions and Kakeya-Nikodym averages

Abstract:  We consider the problem of determining upper bounds on the growth of L^p norms of eigenfunctions of the Laplacian on a compact Riemannian manifold. After an introduction to the problem, we will discuss recent works of C. Sogge and the speaker with C. Sogge relating such growth to mass concentration in frequency dependent tubes about geodesic segments. We then show that this yields improved L^p bounds for manifolds with nonpositive sectional curvatures, extending a result of Sogge-Zelditch to higher dimensions.





 

Date:
-
Location:
745 Patterson Office Tower
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