Numerical Analysis Seminar

Date: October 29, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 624

Speaker: Agnieszka Miedlar, The University of Kansas

Title: The NLFEAST Algorithm for Large-Scale Nonlinear Eigenvalue Problems

Abstract: Eigenvalue problems in which the coefficient matrices depend nonlinearly on the eigenvalues arise in a variety of applications in science and engineering, e.g., dynamic analysis of structures or computational nanoelectronics, to mention just a few. This talk will discuss how the Cauchy integral-based approaches offer an attractive framework for using "spectrum slicing" to develop highly efficient and flexible techniques for solving large-scale nonlinear eigenvalue problems. We will first introduce the nonlinear counterpart of the well-established linear FEAST algorithm. Like its linear predecessor, the nonlinear FEAST (NLFEAST) algorithm can be used to solve nonlinear eigenvalue problems for the eigenpairs corresponding to eigenvalues that lie in a user-specified region in the complex plane, thereby allowing for the calculation of large number of eigenpairs in parallel. To develop a nonlinear FEAST algorithm that enables the iterative refinement of a subspace of a fixed dimension, we propose to use a modified form of the contour integral resulting from the relationship between the NLFEAST and the residual inverse iteration by Neumaier for the nonlinear eigenvalue problems. Finally, we will use several physically-motivated examples to illustrate the method. This is a joint work with B. Gavin, E. Polizzi and Y. Saad.