Publications

Littlewood, David J.; Jones, Reese E.; Plews, Julia A.; Hetmaniuk, Ulrich L.; Lifflander, Jonathan

Abstract not provided.

Hetmaniuk, Ulrich L.; Knupp, Patrick K.

Abstract not provided.

Hetmaniuk, Ulrich L.

Abstract not provided.

Proposed for publication in ACM Transactions on Math Software.

Hetmaniuk, Ulrich L.; Thornquist, Heidi K.; Baker, Christopher G.; Lehoucq, Richard B.

Abstract not provided.

Proposed for publication in the SIAM Journal on Scientific Computing.

Knupp, Patrick K.; Hetmaniuk, Ulrich L.

Abstract not provided.

Hetmaniuk, Ulrich L.; Knupp, Patrick K.

Abstract not provided.

International Journal for Numerical Methods in Engineering

Arbenz, Peter; Hetmaniuk, Ulrich L.; Lehoucq, Richard B.; Tuminaro, Raymond S.

The goal of our paper is to compare a number of algorithms for computing a large number of eigenvectors of the generalized symmetric eigenvalue problem arising from a modal analysis of elastic structures. The shift-invert Lanczos algorithm has emerged as the workhorse for the solution of this generalized eigenvalue problem; however, a sparse direct factorization is required for the resulting set of linear equations. Instead, our paper considers the use of preconditioned iterative methods. We present a brief review of available preconditioned eigensolvers followed by a numerical comparison on three problems using a scalable algebraic multigrid (AMG) preconditioner. Copyright © 2005 John Wiley & Sons, Ltd.

Walsh, Timothy W.; Reese, Garth M.; Hetmaniuk, Ulrich L.

An a posteriori error estimator is developed for the eigenvalue analysis of three-dimensional heterogeneous elastic structures. It constitutes an extension of a well-known explicit estimator to heterogeneous structures. We prove that our estimates are independent of the variations in material properties and independent of the polynomial degree of finite elements. Finally, we study numerically the effectivity of this estimator on several model problems.

Proposed for publication in the SIAM Journal on Matrix Analysis and Applications Special Issue on Accurate Solution of Eigenvalue P.

Hetmaniuk, Ulrich L.; Lehoucq, Richard B.

This paper analyzes the accuracy of the shift-invert Lanczos iteration for computing eigenpairs of the symmetric definite generalized eigenvalue problem. We provide bounds for the accuracy of the eigenpairs produced by shift-invert Lanczos given a residual reduction. We discuss the implications of our analysis for practical shift-invert Lanczos iterations. When the generalized eigenvalue problem arises from a conforming finite element method, we also comment on the uniform accuracy of bounds (independent of the mesh size h).

Hetmaniuk, Ulrich L.; Lehoucq, Richard B.

Abstract not provided.

Lehoucq, Richard B.; Hetmaniuk, Ulrich L.; Hetmaniuk, Ulrich L.

Modal analysis of three-dimensional structures frequently involves finite element discretizations with millions of unknowns and requires computing hundreds or thousands of eigenpairs. In this presentation we review methods based on domain decomposition for such eigenspace computations in structural dynamics. We distinguish approaches that solve the eigenproblem algebraically (with minimal connections to the underlying partial differential equation) from approaches that tightly couple the eigensolver with the partial differential equation.

Hetmaniuk, Ulrich L.

Abstract not provided.