227 research outputs found
Mixed variational formulations of finite element analysis of elastoacoustic/slosh fluid-structure interaction
A general three-field variational principle is obtained for the motion of an acoustic fluid enclosed in a rigid or flexible container by the method of canonical decomposition applied to a modified form of the wave equation in the displacement potential. The general principle is specialized to a mixed two-field principle that contains the fluid displacement potential and pressure as independent fields. This principle contains a free parameter alpha. Semidiscrete finite-element equations of motion based on this principle are displayed and applied to the transient response and free-vibrations of the coupled fluid-structure problem. It is shown that a particular setting of alpha yields a rich set of formulations that can be customized to fit physical and computational requirements. The variational principle is then extended to handle slosh motions in a uniform gravity field, and used to derive semidiscrete equations of motion that account for such effects
Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects
We first briefly report on the status and recent achievements of the ELPA-AEO
(Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and
Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects.
In both collaboratory efforts, scientists from the application areas,
mathematicians, and computer scientists work together to develop and make
available efficient highly parallel methods for the solution of eigenvalue
problems. Then we focus on a topic addressed in both projects, the use of mixed
precision computations to enhance efficiency. We give a more detailed
description of our approaches for benefiting from either lower or higher
precision in three selected contexts and of the results thus obtained
Variational principles for self-adjoint operator functions arising from second-order systems
Variational principles are proved for self-adjoint operator functions arising
from variational evolution equations of the form Here and are densely defined,
symmetric and positive sesquilinear forms on a Hilbert space . We associate
with the variational evolution equation an equivalent Cauchy problem
corresponding to a block operator matrix , the forms where
and are in the domain of the form , and a corresponding
operator family . Using form methods we define a generalized
Rayleigh functional and characterize the eigenvalues above the essential
spectrum of by a min-max and a max-min variational principle. The
obtained results are illustrated with a damped beam equation.Comment: to appear in Operators and Matrice
Simultaneous Reduced Basis Approximation of Parameterized Elliptic Eigenvalue Problems
The focus is on a model reduction framework for parameterized elliptic
eigenvalue problems by a reduced basis method. In contrast to the standard
single output case, one is interested in approximating several outputs
simultaneously, namely a certain number of the smallest eigenvalues. For a fast
and reliable evaluation of these input-output relations, we analyze a
posteriori error estimators for eigenvalues. Moreover, we present different
greedy strategies and study systematically their performance. Special attention
needs to be paid to multiple eigenvalues whose appearance is
parameter-dependent. Our methods are of particular interest for applications in
vibro-acoustics
- …