NDLI: Multigrid preconditioned conjugate-gradient solver for mixed finite-element method

Content Provider	Springer Nature Link
Author	Wilson, John David Naff, Richard L.
Copyright Year	2009
Abstract	The mixed finite-element approximation to a second-order elliptic PDE results in a saddle-point problem and leads to an indefinite linear system of equations. The mixed system of equations can be transformed into coupled symmetric positive-definite matrix equations, or a Schur complement problem, using block Gauss elimination. A preconditioned conjugate-gradient algorithm is used for solving the Schur complement problem. The mixed finite-element method is closely related to the cell-centered finite difference scheme for solving second-order elliptic problems with variable coefficients. For the cell-centered finite difference scheme, a simple multigrid algorithm can be defined and used as a preconditioner. For distorted grids, an additional iteration is needed. Nested iteration with a multigrid preconditioned conjugate gradient inner iteration results in an effective numerical solution technique for the mixed system of linear equations arising from a discretization on distorted grids. Numerical results show that the preconditioned conjugate-gradient inner iteration is robust with respect to grid size and variability in the hydraulic conductivity tensor.
Starting Page	289
Ending Page	299
Page Count	11
File Format	PDF
ISSN	14200597
Journal	Computational Geosciences
Volume Number	14
Issue Number	2
e-ISSN	15731499
Language	English
Publisher	Springer Netherlands
Publisher Date	2009-08-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mixed finite element method Lowest-order Raviart–Thomas Subsurface flow Multigrid Distorted grids Conjugate gradient Nested iteration Mathematical Modeling and Industrial Mathematics Soil Science & Conservation Hydrogeology Geotechnical Engineering
Content Type	Text
Resource Type	Article
Subject	Computers in Earth Sciences Computational Theory and Mathematics Computer Science Applications 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

Multigrid preconditioned conjugate-gradient solver for mixed finite-element method

Multilevel Method for Mixed Eigenproblems

Computational issues of hybrid and multipoint mixed methods for groundwater flow in anisotropic media

Convergence of a symmetric MPFA method on quadrilateral grids

Mixed finite element method on distorted rectangular grids (1994)

Analysis and comparison of mixed finite element and multipoint flux approximation methods for homogeneous media

Deflation accelerated parallel preconditioned conjugate gradient method in finite element.

Compositional flow modeling using a multi-point flux mixed finite element method

Multiscale mixed/mimetic methods on corner-point grids

Multigrid preconditioned conjugate-gradient solver for mixed finite-element method

Similar Documents

Multigrid preconditioned conjugate-gradient solver for mixed finite-element method

Multilevel Method for Mixed Eigenproblems

Computational issues of hybrid and multipoint mixed methods for groundwater flow in anisotropic media

Convergence of a symmetric MPFA method on quadrilateral grids

Mixed finite element method on distorted rectangular grids (1994)

Analysis and comparison of mixed finite element and multipoint flux approximation methods for homogeneous media

Deflation accelerated parallel preconditioned conjugate gradient method in finite element.

Compositional flow modeling using a multi-point flux mixed finite element method

Multiscale mixed/mimetic methods on corner-point grids

Multigrid preconditioned conjugate-gradient solver for mixed finite-element method