Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

Handle URI:
http://hdl.handle.net/10754/598112
Title:
Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems
Authors:
Frohne, Jörg; Heister, Timo; Bangerth, Wolfgang
Abstract:
© 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.
Citation:
Frohne J, Heister T, Bangerth W (2015) Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems. Int J Numer Meth Engng 105: 416–439. Available: http://dx.doi.org/10.1002/nme.4977.
Publisher:
Wiley-Blackwell
Journal:
International Journal for Numerical Methods in Engineering
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
6-Aug-2015
DOI:
10.1002/nme.4977
Type:
Article
ISSN:
0029-5981
Sponsors:
Parts of the work of the first author were supported by the Deutsche Forschungsgemeinschaft (DFG) within Priority Program 1480, ‘Modelling, Simulation and Compensation of Thermal Effects for Complex Machining Processes’, through grant number BL 256/11-3.The third author is supported by the National Science Foundation through award no. OCI-1148116. The second and third authors are supported in part by the Computational Infrastructure in Geodynamics initiative (CIG), through the National Science Foundation under award no. EAR-0949446 and The University of California—Davis. This publication is based in part on the work supported by award no. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).Some computations for this paper were performed on the Brazos and Hurr clusters at the Institute for Applied Mathematics and Computational Science (IAMCS) at Texas A&M University. Part of Brazos was supported by NSF award DMS-0922866. Hurr is supported by award no. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorFrohne, Jörgen
dc.contributor.authorHeister, Timoen
dc.contributor.authorBangerth, Wolfgangen
dc.date.accessioned2016-02-25T13:12:55Zen
dc.date.available2016-02-25T13:12:55Zen
dc.date.issued2015-08-06en
dc.identifier.citationFrohne J, Heister T, Bangerth W (2015) Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems. Int J Numer Meth Engng 105: 416–439. Available: http://dx.doi.org/10.1002/nme.4977.en
dc.identifier.issn0029-5981en
dc.identifier.doi10.1002/nme.4977en
dc.identifier.urihttp://hdl.handle.net/10754/598112en
dc.description.abstract© 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.en
dc.description.sponsorshipParts of the work of the first author were supported by the Deutsche Forschungsgemeinschaft (DFG) within Priority Program 1480, ‘Modelling, Simulation and Compensation of Thermal Effects for Complex Machining Processes’, through grant number BL 256/11-3.The third author is supported by the National Science Foundation through award no. OCI-1148116. The second and third authors are supported in part by the Computational Infrastructure in Geodynamics initiative (CIG), through the National Science Foundation under award no. EAR-0949446 and The University of California—Davis. This publication is based in part on the work supported by award no. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).Some computations for this paper were performed on the Brazos and Hurr clusters at the Institute for Applied Mathematics and Computational Science (IAMCS) at Texas A&M University. Part of Brazos was supported by NSF award DMS-0922866. Hurr is supported by award no. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherWiley-Blackwellen
dc.subjectActive set methoden
dc.subjectAdaptive finite element methodsen
dc.subjectContact problemsen
dc.subjectElastoplasticityen
dc.subjectParallel computingen
dc.titleEfficient numerical methods for the large-scale, parallel solution of elastoplastic contact problemsen
dc.typeArticleen
dc.identifier.journalInternational Journal for Numerical Methods in Engineeringen
dc.contributor.institutionInstitute of Applied Mathematics; Technische Universität Dortmund; 44221 Dortmund Germanyen
dc.contributor.institutionMathematical Sciences; Clemson University; O-110 Martin Hall, Clemson SC 29634-0975 USAen
dc.contributor.institutionDepartment of Mathematics; Texas A&M University; College Station TX 77843-3368 USAen
kaust.grant.numberKUS-C1-016-04en
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