Publications

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Software development for high-performance scientific computing continues to evolve in response to increased parallelism and the advent of on-node accelerators, in particular GPUs. While these hardware advancements have the potential to significantly reduce turnaround times, they also present implementation and design challenges for engineering codes. We investigate the use of two strategies to mitigate these challenges: the Kokkos library for performance portability across disparate architectures, and the DARMA/vt library for asynchronous many-task scheduling. We investigate the application of Kokkos within the NimbleSM finite element code and the LAMÉ constitutive model library. We explore the performance of DARMA/vt applied to NimbleSM contact mechanics algorithms. Software engineering strategies are discussed, followed by performance analyses of relevant solid mechanics simulations which demonstrate the promise of Kokkos and DARMA/vt for accelerated engineering simulators.

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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.

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.

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).

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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.

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