1,271 research outputs found
Local Improvements to Reduced-Order Approximations of Optimal Control Problems Governed by Diffusion-Convection-Reaction Equation
We consider the optimal control problem governed by diffusion convection
reaction equation without control constraints. The proper orthogonal
decomposition(POD) method is used to reduce the dimension of the problem. The
POD method may be lack of accuracy if the POD basis depending on a set of
parameters is used to approximate the problem depending on a different set of
parameters. We are interested in the perturbation of diffusion term. To
increase the accuracy and robustness of the basis, we compute three bases
additional to the baseline POD. The first two of them use the sensitivity
information to extrapolate and expand the POD basis. The other one is based on
the subspace angle interpolation method. We compare these different bases in
terms of accuracy and complexity and investigate the advantages and main
drawbacks of them.Comment: 19 pages, 5 figures, 2 table
Goal-oriented h-adaptivity for the Helmholtz equation: error estimates, local indicators and refinement strategies
The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-010-0557-2This paper introduces a new goal-oriented adaptive technique based on a simple and effective post-process of the finite element approximations. The goal-oriented character of the estimate is achieved by analyzing both the direct problem and an auxiliary problem, denoted as adjoint or dual problem, which is related to the quantity of interest. Thus, the error estimation technique proposed in this paper would fall into the category of recovery-type explicit residual a posteriori error estimates. The procedure is valid for general linear quantities of interest and it is also extended to non-linear ones. The numerical examples demonstrate the efficiency of the proposed approach and discuss: (1) different error representations, (2) assessment of the dispersion error, and (3) different remeshing criteria.Peer ReviewedPostprint (author's final draft
Formulation and optimization of the energy-based blended quasicontinuum method
We formulate an energy-based atomistic-to-continuum coupling method based on
blending the quasicontinuum method for the simulation of crystal defects. We
utilize theoretical results from Ortner and Van Koten (manuscript) to derive
optimal choices of approximation parameters (blending function and finite
element grid) for microcrack and di-vacancy test problems and confirm our
analytical predictions in numerical tests
- …