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An Optimal Domain Decomposition Method for the C-Grid Navier-Stokes Jacobian

Thies, Jonas and Baars, Sven and van der Klok, Mark and Wubs, Fred W. (2017) An Optimal Domain Decomposition Method for the C-Grid Navier-Stokes Jacobian. GAMM Workshop on Applied and Numerical Linear Algebra, 7.-8. Sep 2017, University of Cologne, Germany. (Unpublished)

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Official URL: http://gamm-workshop.uni-koeln.de/15960.html

Abstract

The Arakawa C-grid scheme is perhaps the most well-known discretization of the incompressible Navier-Stokes equations. The different variables (velocity components and pressure) are placed on the faces and in the center of the grid cells, respectively, to achieve good conservation and stability properties. In [De Niet and Wubs, IMA J. Num Anal. 2009] an optimal ordering of the variables for the sequential LU-decomposition of the resulting Jacobian was developed based on observations how fill is generated for such matrices during Gaussian elimination. In [Wubs and Thies, S!MAX 2011] the method was used in a domain decomposition approach and extended by a robust dropping strategy that leads to a preconditioner achieving a grid-independent convergence rate of GMRES. Structure-preserving properties of this incomplete LU (ILU) factorization allow recursive application and achieving optimal complexity of O(N log N) for scalar problems already. In this talk we show that this goal can be achieved for the 3D C-grid Navier-Stokes equations as well by using a special choice of space-filling subdomain shapes (parallelepipeda). We demonstrate results with this novel partitioning approach for both direct factorization and the multi-level ILU method on several thousand CPU cores. Possible applications include fully implicit time integration and bifurcation analysis of fluid dynamics problems.

Item URL in elib:https://elib.dlr.de/116849/
Document Type:Conference or Workshop Item (Speech)
Title:An Optimal Domain Decomposition Method for the C-Grid Navier-Stokes Jacobian
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Thies, JonasJonas.Thies (at) dlr.deUNSPECIFIED
Baars, Svens.baars (at) rug.nlUNSPECIFIED
van der Klok, Markmlvanderklok (at) gmail.comUNSPECIFIED
Wubs, Fred W.f.w.wubs (at) rug.nlUNSPECIFIED
Date:7 September 2017
Refereed publication:No
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Unpublished
Keywords:Saddlepoint matrix, incomplete factorization, Arakawa C-Grid, Multi-level
Event Title:GAMM Workshop on Applied and Numerical Linear Algebra
Event Location:University of Cologne, Germany
Event Type:Workshop
Event Dates:7.-8. Sep 2017
Organizer:Universität zu Köln
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Technik für Raumfahrtsysteme
DLR - Research theme (Project):R - Vorhaben SISTEC
Location: Köln-Porz
Institutes and Institutions:Institut of Simulation and Software Technology
Institut of Simulation and Software Technology > High Performance Computing
Deposited By: Thies, Jonas
Deposited On:12 Jan 2018 12:08
Last Modified:31 Jul 2019 20:14

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