Projection Based Multiscale Optimization Method for Eigenvalue Problems

Graf, P A; Jones, W B

doi:10.1007/s10898-007-9135-3

Title: Projection Based Multiscale Optimization Method for Eigenvalue Problems

Full Record
Other Related Research

Abstract

We present a projection based multiscale optimization method for eigenvalue problems. In multiscale optimization, optimization steps using approximations at a coarse scale alternate with corrections by occasional calculations at a finer scale. We study an example in the context of electronic structure optimization. Theoretical analysis and numerical experiments provide estimates of the expected efficiency and guidelines for parameter selection.

Authors:: Graf, P A; Jones, W B

Publication Date:: Mon Jan 01 00:00:00 EST 2007

Research Org.:: National Renewable Energy Lab. (NREL), Golden, CO (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 976976

DOE Contract Number:: AC36-08GO28308

Resource Type:: Journal Article

Journal Name:: Journal of Global Optimization

Additional Journal Information:: Journal Volume: 39; Journal Issue: 2007

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; APPROXIMATIONS; EFFICIENCY; EIGENVALUES; ELECTRONIC STRUCTURE; OPTIMIZATION; RECOMMENDATIONS; Computational Sciences

Citation Formats


                    Graf, P A, and Jones, W B. Projection Based Multiscale Optimization Method for Eigenvalue Problems.  United States: N. p., 2007. 
        Web.  doi:10.1007/s10898-007-9135-3.

Copy to clipboard


                    Graf, P A, & Jones, W B. Projection Based Multiscale Optimization Method for Eigenvalue Problems.  United States.  https://doi.org/10.1007/s10898-007-9135-3

Copy to clipboard


                    Graf, P A, and Jones, W B. 2007.  
        "Projection Based Multiscale Optimization Method for Eigenvalue Problems".  United States.  https://doi.org/10.1007/s10898-007-9135-3.

Copy to clipboard


                    
@article{osti_976976,

  title        = {Projection Based Multiscale Optimization Method for Eigenvalue Problems},

  author       = {Graf, P A and Jones, W B},

  abstractNote = {We present a projection based multiscale optimization method for eigenvalue problems. In multiscale optimization, optimization steps using approximations at a coarse scale alternate with corrections by occasional calculations at a finer scale. We study an example in the context of electronic structure optimization. Theoretical analysis and numerical experiments provide estimates of the expected efficiency and guidelines for parameter selection.},

  doi          = {10.1007/s10898-007-9135-3},

  url          = {https://www.osti.gov/biblio/976976},
  journal      = {Journal of Global Optimization},
number       = 2007,

  volume       = 39,

  place        = {United States},

  year         = {Mon Jan 01 00:00:00 EST 2007},

  month        = {Mon Jan 01 00:00:00 EST 2007}

}

Copy to clipboard

Journal Article:

https://doi.org/10.1007/s10898-007-9135-3

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem

Journal Article Jeong, Yongjin; Park, Jinsu; Lee, Hyun; ... - Journal of Computational Physics

In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also notedmore »« less
https://doi.org/10.1016/J.JCP.2015.09.004
An Analysis Platform for Multiscale Hydrogeologic Modeling with Emphasis on Hybrid Multiscale Methods

Journal Article Scheibe, Timothy; Murphy, Ellyn; Chen, Xingyuan; ... - Ground Water

One of the most significant challenges faced by hydrogeologic modelers is the disparity between the spatial and temporal scales at which fundamental flow, transport, and reaction processes can best be understood and quantified (e.g., microscopic to pore scales and seconds to days) and at which practical model predictions are needed (e.g., plume to aquifer scales and years to centuries). While the multiscale nature of hydrogeologic problems is widely recognized, technological limitations in computation and characterization restrict most practical modeling efforts to fairly coarse representations of heterogeneous properties and processes. For some modern problems, the necessary level of simplification is suchmore »« less
Cited by 57
https://doi.org/10.1111/gwat.12179

Full Text Available
An Analysis Platform for Multiscale Hydrogeologic Modeling with Emphasis on Hybrid Multiscale Methods

Journal Article Scheibe, Timothy; Murphy, Ellyn; Chen, Xingyuan; ... - Ground Water, 53(1):38-56

One of the most significant challenges facing hydrogeologic modelers is the disparity between those spatial and temporal scales at which fundamental flow, transport and reaction processes can best be understood and quantified (e.g., microscopic to pore scales, seconds to days) and those at which practical model predictions are needed (e.g., plume to aquifer scales, years to centuries). While the multiscale nature of hydrogeologic problems is widely recognized, technological limitations in computational and characterization restrict most practical modeling efforts to fairly coarse representations of heterogeneous properties and processes. For some modern problems, the necessary level of simplification is such that modelmore »« less
https://doi.org/10.1111/gwat.12179
Convergence Analysis of a Locally Accelerated Preconditioned Steepest Descent Method for Hermitian-Definite Generalized Eigenvalue Problems

Journal Article Cai, Yunfeng; Bai, Zhaojun; Pask, John E.; ... - Journal of Computational Mathematics

By extending the classical analysis techniques due to Samokish, Faddeev and Faddeeva, and Longsine and McCormick among others, we prove the convergence of preconditioned steepest descent with implicit deflation (PSD-id) method for solving Hermitian-definite generalized eigenvalue problems. Moreover, we derive a nonasymptotic estimate of the rate of convergence of the PSD-id method. We show that with a proper choice of the shift, the indefinite shift-and-invert preconditioner is a locally accelerated preconditioner, and is asymptotically optimal that leads to superlinear convergence. Numerical examples are presented to verify the theoretical results on the convergence behavior of the PSDid method for solving ill-conditionedmore »« less
Cited by 1
https://doi.org/10.4208/jcm.1703-m2016-0580

Full Text Available
A variational multiscale immersed meshfree method for heterogeneous materials

Journal Article Huang, Tsung-Hui; Chen, Jiun-Shyan; Tupek, Michael; ... - Computational Mechanics

Abstract We introduce an immersed meshfree formulation for modeling heterogeneous materials with flexible non-body-fitted discretizations, approximations, and quadrature rules. The interfacial compatibility condition is imposed by a volumetric constraint, which avoids a tedious contour integral for complex material geometry. The proposed immersed approach is formulated under a variational multiscale based formulation, termed the variational multiscale immersed method (VMIM). Under this framework, the solution approximation on either the foreground or the background can be decoupled into coarse-scale and fine-scale in the variational equations, where the fine-scale approximation represents a correction to the residual of the coarse-scale equations. The resulting fine-scale solutionmore »« less
https://doi.org/10.1007/s00466-020-01968-1

Similar Records