Author: Institute for Computer Applications in Science and EngineeringPublisher:
ISBN:
Category :
Languages : en
Pages : 26
Book Description
A Robust Multilevel Simultaneous Eigenvalue Solver
Author: Institute for Computer Applications in Science and EngineeringPublisher:
ISBN:
Category :
Languages : en
Pages : 26
Book Description
A Robust Multilevel Simultaneous Eigenvalue Solver
Author: National Aeronautics and Space Administration NASAPublisher:
ISBN: 9781729141717
Category :
Languages : en
Pages : 26
Book Description
Multilevel (ML) algorithms for eigenvalue problems are often faced with several types of difficulties such as: the mixing of approximated eigenvectors by the solution process, the approximation of incomplete clusters of eigenvectors, the poor representation of solution on coarse levels, and the existence of close or equal eigenvalues. Algorithms that do not treat appropriately these difficulties usually fail, or their performance degrades when facing them. These issues motivated the development of a robust adaptive ML algorithm which treats these difficulties, for the calculation of a few eigenvectors and their corresponding eigenvalues. The main techniques used in the new algorithm include: the adaptive completion and separation of the relevant clusters on different levels, the simultaneous treatment of solutions within each cluster, and the robustness tests which monitor the algorithm's efficiency and convergence. The eigenvectors' separation efficiency is based on a new ML projection technique generalizing the Rayleigh Ritz projection, combined with a technique, the backrotations. These separation techniques, when combined with an FMG formulation, in many cases lead to algorithms of O(qN) complexity, for q eigenvectors of size N on the finest level. Previously developed ML algorithms are less focused on the mentioned difficulties. Moreover, algorithms which employ fine level separation techniques are of O(q(sub 2)N) complexity and usually do not overcome all these difficulties. Computational examples are presented where Schrodinger type eigenvalue problems in 2-D and 3-D, having equal and closely clustered eigenvalues, are solved with the efficiency of the Poisson multigrid solver. A second order approximation is obtained in O(qN) work, where the total computational work is equivalent to only a few fine level relaxations per eigenvector. Costiner, Sorin and Taasan, Shlomo Langley Research Center NAS1-19480; NAS1-18605; RTOP 505-90-52-01...
Scientific and Technical Aerospace Reports
Author: Proceedings of the Cornelius Lanczos International Centenary Conference
Author: J. David BrownPublisher: SIAM
ISBN: 9780898713398
Category : Biography & Autobiography
Languages : en
Pages : 722
Book Description
The Algebraic Multigrid Projection for Eigenvalue Problems; Backrotations and Multigrid Fixed Points
Author: Sorin CostinerPublisher:
ISBN:
Category : Algebra
Languages : en
Pages : 24
Book Description
Monthly Catalog of United States Government Publications
Author: Monthly Catalogue, United States Public Documents
Author: Publisher:
ISBN:
Category : Government publications
Languages : en
Pages : 752
Book Description
Multigrid Techniques for Nonlinear Eigenvalue Probems: Solutions of a Nonlinear Schroedinger Eigenvalue Problem in 2D and 3D
Author: Government Reports Annual Index
Author: Publisher:
ISBN:
Category : Research
Languages : en
Pages : 1290
Book Description
Sections 1-2. Keyword Index.--Section 3. Personal author index.--Section 4. Corporate author index.-- Section 5. Contract/grant number index, NTIS order/report number index 1-E.--Section 6. NTIS order/report number index F-Z.
Numerical Methods for Large Eigenvalue Problems
Author: Yousef SaadPublisher: SIAM
ISBN: 9781611970739
Category : Mathematics
Languages : en
Pages : 292
Book Description
This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.