Structure-Preserving Algorithms for Solving Large Scale Eigenvalue Problems

University Of California-Davis, Davis CA

Investigators

Abstract

Optimization of large scale eigenvalue computations is a long-standing problem in computational mathematics and scientific computing community. In this project, the PI and his collaborators will develop novel structure-preserving algorithms for accurately and efficiently solving large scale eigenvalue problems. Specifically, they will focus on large scale eigenvalue problems of structured matrix pencils, quadratic eigenvalue problems and nonlinear eigenvalue problems. They will study structure-preserving Rayleight-Ritz subspace projection techniques for solving these eigenvalue problems, that include the multi-level orthogonalization process of Krylov subspaces, second-order Arnoldi (SOAR) method and the nonlinear Arnoldi method. The goal of the project represents a significant advance in a frontier area of scientific endeavor and engineering design through the application of computational mathematics and simulations. The target applications include these types of eigenvalue problems arising from simulations of electrical circuits and MEMS devices, finite element analysis of structure dynamics, acoustics and electromagnetics. These applications are of great technology importance for next-generation electronics, automobile efficiency and safety and energy-efficiency monitoring devices and others. The results of this project will be both the description of effective computational simulation strategies for these problems and also software made publicly available.