Application of PDSLin to the magnetic reconnection problem

Handle URI:
http://hdl.handle.net/10754/562603
Title:
Application of PDSLin to the magnetic reconnection problem
Authors:
Yuan, Xuefei; Li, Xiaoyesherry; Yamazaki, Ichitaro; Jardin, Stephen C.; Koniges, Alice E.; Keyes, David E. ( 0000-0002-4052-7224 )
Abstract:
Magnetic reconnection is a fundamental process in a magnetized plasma at both low and high magnetic Lundquist numbers (the ratio of the resistive diffusion time to the Alfvén wave transit time), which occurs in a wide variety of laboratory and space plasmas, e.g. magnetic fusion experiments, the solar corona and the Earth's magnetotail. An implicit time advance for the two-fluid magnetic reconnection problem is known to be difficult because of the large condition number of the associated matrix. This is especially troublesome when the collisionless ion skin depth is large so that the Whistler waves, which cause the fast reconnection, dominate the physics (Yuan et al 2012 J. Comput. Phys. 231 5822-53). For small system sizes, a direct solver such as SuperLU can be employed to obtain an accurate solution as long as the condition number is bounded by the reciprocal of the floating-point machine precision. However, SuperLU scales effectively only to hundreds of processors or less. For larger system sizes, it has been shown that physics-based (Chacón and Knoll 2003 J. Comput. Phys. 188 573-92) or other preconditioners can be applied to provide adequate solver performance. In recent years, we have been developing a new algebraic hybrid linear solver, PDSLin (Parallel Domain decomposition Schur complement-based Linear solver) (Yamazaki and Li 2010 Proc. VECPAR pp 421-34 and Yamazaki et al 2011 Technical Report). In this work, we compare numerical results from a direct solver and the proposed hybrid solver for the magnetic reconnection problem and demonstrate that the new hybrid solver is scalable to thousands of processors while maintaining the same robustness as a direct solver. © 2013 IOP Publishing Ltd.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Extreme Computing Research Center
Publisher:
IOP Publishing
Journal:
Computational Science and Discovery
Issue Date:
1-Jan-2013
DOI:
10.1088/1749-4699/6/1/014002
Type:
Article
ISSN:
17494680
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorYuan, Xuefeien
dc.contributor.authorLi, Xiaoyesherryen
dc.contributor.authorYamazaki, Ichitaroen
dc.contributor.authorJardin, Stephen C.en
dc.contributor.authorKoniges, Alice E.en
dc.contributor.authorKeyes, David E.en
dc.date.accessioned2015-08-03T10:58:02Zen
dc.date.available2015-08-03T10:58:02Zen
dc.date.issued2013-01-01en
dc.identifier.issn17494680en
dc.identifier.doi10.1088/1749-4699/6/1/014002en
dc.identifier.urihttp://hdl.handle.net/10754/562603en
dc.description.abstractMagnetic reconnection is a fundamental process in a magnetized plasma at both low and high magnetic Lundquist numbers (the ratio of the resistive diffusion time to the Alfvén wave transit time), which occurs in a wide variety of laboratory and space plasmas, e.g. magnetic fusion experiments, the solar corona and the Earth's magnetotail. An implicit time advance for the two-fluid magnetic reconnection problem is known to be difficult because of the large condition number of the associated matrix. This is especially troublesome when the collisionless ion skin depth is large so that the Whistler waves, which cause the fast reconnection, dominate the physics (Yuan et al 2012 J. Comput. Phys. 231 5822-53). For small system sizes, a direct solver such as SuperLU can be employed to obtain an accurate solution as long as the condition number is bounded by the reciprocal of the floating-point machine precision. However, SuperLU scales effectively only to hundreds of processors or less. For larger system sizes, it has been shown that physics-based (Chacón and Knoll 2003 J. Comput. Phys. 188 573-92) or other preconditioners can be applied to provide adequate solver performance. In recent years, we have been developing a new algebraic hybrid linear solver, PDSLin (Parallel Domain decomposition Schur complement-based Linear solver) (Yamazaki and Li 2010 Proc. VECPAR pp 421-34 and Yamazaki et al 2011 Technical Report). In this work, we compare numerical results from a direct solver and the proposed hybrid solver for the magnetic reconnection problem and demonstrate that the new hybrid solver is scalable to thousands of processors while maintaining the same robustness as a direct solver. © 2013 IOP Publishing Ltd.en
dc.publisherIOP Publishingen
dc.titleApplication of PDSLin to the magnetic reconnection problemen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalComputational Science and Discoveryen
dc.contributor.institutionLawrence Berkeley National Laboratory, Berkeley, CA 94720, United Statesen
dc.contributor.institutionInnovative Computing Laboratory, University of Tennessee, Knoxville, TN 37996, United Statesen
dc.contributor.institutionTheory and Computation Department, Princeton Plasma Physics Laboratory, Princeton, NJ 08540, United Statesen
dc.contributor.institutionDepartment of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, United Statesen
dc.contributor.institutionDepartment of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, United Statesen
kaust.authorKeyes, David E.en
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