TY - JOUR

T1 - Application of PDSLin to the magnetic reconnection problem

AU - Yuan, Xuefei

AU - Li, Xiaoyesherry

AU - Yamazaki, Ichitaro

AU - Jardin, Stephen C.

AU - Koniges, Alice E.

AU - Keyes, David E.

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2013/1/9

Y1 - 2013/1/9

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/562603

UR - https://iopscience.iop.org/article/10.1088/1749-4699/6/1/014002

UR - http://www.scopus.com/inward/record.url?scp=84875405686&partnerID=8YFLogxK

U2 - 10.1088/1749-4699/6/1/014002

DO - 10.1088/1749-4699/6/1/014002

M3 - Article

SN - 1749-4680

VL - 6

SP - 014002

JO - Computational Science and Discovery

JF - Computational Science and Discovery

IS - 1

ER -