skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Teko: A block preconditioning capability with concrete example applications in Navier--Stokes and MHD

Abstract

This study describes the design of Teko, an object-oriented C++ library for implementing advanced block preconditioners. Mathematical design criteria that elucidate the needs of block preconditioning libraries and techniques are explained and shown to motivate the structure of Teko. For instance, a principal design choice was for Teko to strongly reflect the mathematical statement of the preconditioners to reduce development burden and permit focus on the numerics. Additional mechanisms are explained that provide a pathway to developing an optimized production capable block preconditioning capability with Teko. Finally, Teko is demonstrated on fluid flow and magnetohydrodynamics applications. In addition to highlighting the features of the Teko library, these new results illustrate the effectiveness of recent preconditioning developments applied to advanced discretization approaches.

Authors:
 [1];  [1];  [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1335470
Report Number(s):
SAND-2016-0191J
Journal ID: ISSN 1064-8275; 618821
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 38; Journal Issue: 5; Journal ID: ISSN 1064-8275
Publisher:
SIAM
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Cyr, Eric C., Shadid, John N., and Tuminaro, Raymond S. Teko: A block preconditioning capability with concrete example applications in Navier--Stokes and MHD. United States: N. p., 2016. Web. doi:10.1137/15M1017946.
Cyr, Eric C., Shadid, John N., & Tuminaro, Raymond S. Teko: A block preconditioning capability with concrete example applications in Navier--Stokes and MHD. United States. https://doi.org/10.1137/15M1017946
Cyr, Eric C., Shadid, John N., and Tuminaro, Raymond S. 2016. "Teko: A block preconditioning capability with concrete example applications in Navier--Stokes and MHD". United States. https://doi.org/10.1137/15M1017946. https://www.osti.gov/servlets/purl/1335470.
@article{osti_1335470,
title = {Teko: A block preconditioning capability with concrete example applications in Navier--Stokes and MHD},
author = {Cyr, Eric C. and Shadid, John N. and Tuminaro, Raymond S.},
abstractNote = {This study describes the design of Teko, an object-oriented C++ library for implementing advanced block preconditioners. Mathematical design criteria that elucidate the needs of block preconditioning libraries and techniques are explained and shown to motivate the structure of Teko. For instance, a principal design choice was for Teko to strongly reflect the mathematical statement of the preconditioners to reduce development burden and permit focus on the numerics. Additional mechanisms are explained that provide a pathway to developing an optimized production capable block preconditioning capability with Teko. Finally, Teko is demonstrated on fluid flow and magnetohydrodynamics applications. In addition to highlighting the features of the Teko library, these new results illustrate the effectiveness of recent preconditioning developments applied to advanced discretization approaches.},
doi = {10.1137/15M1017946},
url = {https://www.osti.gov/biblio/1335470}, journal = {SIAM Journal on Scientific Computing},
issn = {1064-8275},
number = 5,
volume = 38,
place = {United States},
year = {Thu Oct 27 00:00:00 EDT 2016},
month = {Thu Oct 27 00:00:00 EDT 2016}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 7 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

A Relaxed Dimensional Factorization preconditioner for the incompressible Navier–Stokes equations
journal, July 2011


An Augmented Lagrangian‐Based Approach to the Oseen Problem
journal, January 2006


Scalable parallel implicit solvers for 3D magnetohydrodynamics
journal, July 2008


A 2D high-β Hall MHD implicit nonlinear solver
journal, July 2003


An Implicit, Nonlinear Reduced Resistive MHD Solver
journal, May 2002


An object-oriented framework for block preconditioning
journal, June 1998


Stabilization and scalable block preconditioning for the Navier–Stokes equations
journal, January 2012


A New Approximate Block Factorization Preconditioner for Two-Dimensional Incompressible (Reduced) Resistive MHD
journal, January 2013


Block Preconditioners Based on Approximate Commutators
journal, January 2006


A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier–Stokes equations
journal, January 2008


A parallel block multi-level preconditioner for the 3D incompressible Navier–Stokes equations
journal, May 2003


An overview of the Trilinos project
journal, September 2005


Playa: High-Performance Programmable Linear Algebra
journal, January 2012


Towards Extreme-Scale Simulations for Low Mach Fluids with Second-Generation Trilinos
journal, December 2014


Performance of fully coupled algebraic multilevel domain decomposition preconditioners for incompressible flow and transport
journal, January 2006


Preconditioned iterative methods for Stokes flow problems arising in computational geodynamics
journal, December 2008


A Note on Preconditioning for Indefinite Linear Systems
journal, January 2000


A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows
journal, October 1972


A Block Preconditioner for an Exact Penalty Formulation for Stationary MHD
journal, January 2014


Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
journal, October 2010


Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG
journal, June 2016


Works referencing / citing this record:

FEMPAR: An Object-Oriented Parallel Finite Element Framework
journal, October 2017


A Computational Architecture for Coupling Heterogeneous Numerical Models and Computing Coupled Derivatives
journal, August 2018