Parallel Newton-Krylov-Schwarz algorithms for the three-dimensional Poisson-Boltzmann equation in numerical simulation of colloi

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 NKSbased PBE solver. In addition, a truly three-dimensional case, which models the interaction between two charged spherical particl...

• Type: Journal
• Year: 2010
• Where: CPHYSICS
• Authors: Feng-Nan Hwang, Shang-Rong Cai, Yun-Long Shao, Jong-Shinn Wu
• Keywords: Colloidal Particles, CPHYSICS 2010, Linear Solver, Poisson-Boltzmann Equation