Computational Materials Chemistry Group, Lehrstuhl für Anorganische Chemie 2 , Ruhr-Universität Bochum , 44780 Bochum , Germany.
J Chem Theory Comput. 2019 Feb 12;15(2):1293-1301. doi: 10.1021/acs.jctc.8b00774. Epub 2019 Feb 4.
The electrostatic problem defined by the continuum solvation models used in molecular mechanics and ab initio molecular dynamics is solved in real space through multiscale methods. First, the Poisson equation is rewritten as a stationary convection-diffusion equation and discretized by a general mesh size fourth-order compact difference scheme. Then, the linear system associated with such a discrete version of the elliptic partial differential equation is solved by a parallel (geometric) multigrid solver whose convergence rates and robustness are improved by an iterant recombination technique in which the multigrid acts as a preconditioner of a Krylov subspace method. The numerical tests performed on ideal and physical systems described by linear Poisson equations under different boundary conditions show the good performance of this accelerated multigrid solver. Furthermore, nonlinear Poisson equations, like the regular modified Poisson-Boltzmann equation, can also be solved by using in addition simple iterative schemes.
通过多尺度方法在实空间中求解分子力学和从头算分子动力学中使用的连续溶剂化模型所定义的静电问题。首先，将泊松方程重写为定常对流扩散方程，并通过通用网格大小四阶紧致差分格式离散化。然后，通过并行（几何）多重网格求解器求解与这种离散椭圆偏微分方程相关的线性系统，其收敛速度和鲁棒性通过迭代重组合技术得到提高，其中多重网格作为 Krylov 子空间方法的预条件器。在不同边界条件下由线性泊松方程描述的理想和物理系统上进行的数值测试表明了这种加速多重网格求解器的良好性能。此外，还可以通过使用简单的迭代方案来求解非线性泊松方程，例如正则修正泊松-玻尔兹曼方程。
