標題: Parallel Newton-Krylov-Schwarz algorithms for the three-dimensional Poisson-Boltzmann equation in numerical simulation of colloidal particle interactions
作者: Hwang, Feng-Nan
Cai, Shang-Rong
Shao, Yun-Long
Wu, Jong-Shinn
機械工程學系
Department of Mechanical Engineering
關鍵字: Poisson-Boltzmann equation;Overlapping Schwarz preconditioning;Inexact Newton;Finite element;Parallel processing;Colloidal particles
公開日期: 1-九月-2010
摘要: We investigate fully parallel Newton-Krylov-Schwarz (NKS) algorithms for solving the large sparse nonlinear systems of equations arising from the finite element discretization of the three-dimensional Poisson-Boltzmann equation (PBE), which is often used to describe the colloidal phenomena of an electric double layer around charged objects in colloidal and interfacial science. The NKS algorithm employs an inexact Newton method with backtracking (INB) as the nonlinear solver in conjunction with a Krylov subspace method as the linear solver for the corresponding Jacobian system. An overlapping Schwarz method as a preconditioner to accelerate the convergence of the linear solver. Two test cases including two isolated charged particles and two colloidal particles in a cylindrical pore are used as benchmark problems to validate the correctness of our parallel NKS-based PBE solver. In addition, a truly three-dimensional case, which models the interaction between two charged spherical particles within a rough charged micro-capillary, is simulated to demonstrate the applicability of our PBE solver to handle a problem with complex geometry. Finally, based on the result obtained from a PC cluster of parallel machines, we show numerically that NKS is quite suitable for the numerical simulation of interaction between colloidal particles, since NKS is robust in the sense that INB is able to converge within a small number of iterations regardless of the geometry, the mesh size, the number of processors. With help of an additive preconditioned Krylov subspace method NKS achieves parallel efficiency of 71% or better on up to a hundred processors for a 3D problem with 5 million unknowns. (C) 2010 Elsevier B.V. All rights reserved.
URI: http://dx.doi.org/10.1016/j.cpc.2010.05.003
http://hdl.handle.net/11536/32263
ISSN: 0010-4655
DOI: 10.1016/j.cpc.2010.05.003
期刊: COMPUTER PHYSICS COMMUNICATIONS
Volume: 181
Issue: 9
起始頁: 1529
結束頁: 1537
顯示於類別:期刊論文


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  1. 000280873500006.pdf