Hierarchical Parallelism for Transient Solid Mechanics Simulations
Abstract not provided.
Publications
An R-adaptive Mesh Optimization Algorithm Based on Interpolation Error Bounds
Abstract not provided.
Eigenspace Computations in Linear Structural Dynamics
Abstract not provided.
Anasazi software for the numerical solution of large-scale eigenvalue problems
Proposed for publication in ACM Transactions on Math Software.
Abstract not provided.
Local 2D metrics for mesh optimization in the target-matrix paradigm
Proposed for publication in the SIAM Journal on Scientific Computing.
Abstract not provided.
The role of mesh quality in theoretical bounds for finite elements: a survey
Abstract not provided.
A comparison of eigensolvers for large-scale 3D modal analysis using AMG-preconditioned iterative methods
International Journal for Numerical Methods in Engineering
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.
Explicit a posteriori error estimates for eigenvalue analysis of heterogeneous elastic structures
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.
Uniform accuracy of eigenpairs from a shift-invert Lanczos method
Proposed for publication in the SIAM Journal on Matrix Analysis and Applications Special Issue on Accurate Solution of Eigenvalue P.
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).
A new Rayleigh quotient minimization algorithm based on algebraic multigrid
Abstract not provided.
Multilevel methods for eigenspace computations in structural dynamics
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.
A posterior error estimates for eigenvalue analysis of heterogeneous elastic structures
Abstract not provided.
12 Results