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Texas A&M University

Colloquium - Agnieszka Miedlar

Date: December 7, 2018

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Agnieszka Miedlar, University of Kansas


Description: Title: Challenges for Eigenvalue Computations in Breakthrough Applications
Abstract: Many real life problems lead to challenging PDE eigenvalue problems, e.g., vibrations of structures or calculation of energy levels in quantum mechanics. A lot of research is devoted to the so-called Adaptive Finite Element Method (AFEM) which allows discretization of the governing PDE, solving the finite dimensional algebraic eigenvalue problem and iteratively improving obtained numerical approximations. However, advanced approaches dedicated to solve these challenging eigenvalue problems require a unified framework bringing together: spectral and perturbation theory to derive a priori error estimators, a posteriori error analysis which enables deriving efficient and reliable error estimators which take into account various errors of different origins, iterative solvers and model reduction techniques to efficiently solve finite dimensional algebraic linear and nonlinear eigenvalue problems etc. This talk will discuss several attempts to achieve the above goal. In particular, we will explain how the Cauchy integral-based approaches offer an attractive algorithmic framework when solving interior large-scale linear and nonlinear eigenvalue problems. Finally, we will illustrate presented methods with several numerical examples.