NDLI: A Two-Level Preconditioner for Schrdinger-Type Singular Elliptic Operator

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Maliassov, Serguei
Copyright Year	1998
Abstract	In this paper a two-level preconditioner is considered for the Schrdinger-type singular operator on a uniform grid on a rectangle. The construction of such preconditioners for a positive definite operator is well defined provided that a restriction of the operator into any subdomain of computational domain is at least positive semidefinite. It is shown that although local matrices approximating the Schrdinger operator on some subdomains are indefinite it is still possible to develop a multilevel preconditioner, which is spectrally equivalent to the operator of the problem.First, explicit estimates of condition number are established for a two-level preconditioner. The main idea of the two-level estimate is to analyze a superelement-based method for a problem with indefinite local superelement matrices, modify the main diagonals of the local matrices sothat they are positive definite and still sum up to the same global matrix. This modification is for theoretical purposes only and does not affect the computational method itself. A generalization of the usual two-level method is considered in which different bilinear forms are defined on the coarse and fine levels. Then, the two-level method can be extended to a multilevel one using the standard theory of multilevel methods with inner iterative procedures.
Starting Page	217
Ending Page	229
Page Count	13
File Format	PDF
ISSN	00361429
DOI	10.1137/S0036142994275056
e-ISSN	10957170
Issue Number	1
Volume Number	35
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	Solution of discretized equations Iterative methods for linear systems two-level preconditioner superelement analysis iterative method Multigrid methods; domain decomposition Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods multilevel substructuring preconditioner Schrdinger equation
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in