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http://dx.doi.org/10.7734/COSEIK.2021.34.4.191

Induced Charge Distribution Using Accelerated Uzawa Method  

Kim, Jae-Hyun (DIT Center, Samsung Electronics)
Jo, Gwanghyun (Department of Mathematics, Kunsan National University)
Ha, Youn Doh (Department of Naval Architecture and Ocean Engineering, Kunsan National University)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.34, no.4, 2021 , pp. 191-197 More about this Journal
Abstract
To calculate the induced charge of atoms in molecular dynamics, linear equations for the induced charges need to be solved. As induced charges are determined at each time step, the process involves considerable computational costs. Hence, an efficient method for calculating the induced charge distribution is required when analyzing large systems. This paper introduces the Uzawa method for solving saddle point problems, which occur in linear systems, for the solution of the Lagrange equation with constraints. We apply the accelerated Uzawa algorithm, which reduces computational costs noticeably using the Schur complement and preconditioned conjugate gradient methods, in order to overcome the drawback of the Uzawa parameter, which affects the convergence speed, and increase the efficiency of the matrix operation. Numerical models of molecular dynamics in which two gold nanoparticles are placed under external electric fields reveal that the proposed method provides improved results in terms of both convergence and efficiency. The computational cost was reduced by approximately 1/10 compared to that for the Gaussian elimination method, and fast convergence of the conjugate gradient, as compared to the basic Uzawa method, was verified.
Keywords
molecular dynamics; induced charge; saddle point problem; uzawa method; preconditioned conjugate gradient;
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