本项目拟对近几年提出的一种区域球状分解法展开研究，该方法被用于数值求解量子化学中的隐式溶剂化模型。由于它在求解类导体屏蔽模型中的优异表现，现已被集成到著名的量子化学软件Gaussian中。而且，最新的研究已经将该区域球状分解法推广到求解线性泊松-玻尔兹曼模型。在本项目中，申请人计划首先将该区域分解法推广到各向异性的极化连续介质模型，并通过数值模拟对比它与其他同类算法的优劣；其次，鉴于该方法在数值求解类导体屏蔽模型时的快速收敛，我们将致力于理论证明该区域球状分解法在三维空间中的收敛性；最后，我们计划将基于区域球状分解法的泊松-玻尔兹曼求解器应用在分子动力学中，以期获得更好的模拟效果。

In this project, we will study a particular domain decomposition method for the implicit solvation models in quantum chemistry, which has been developed in the past several years. Due to its impressive performance for the conductor-like screening model, this method has been integrated to the famous software Gaussian. Furthermore, it has been recently generalized to the linearized Poisson-Boltzmann solvation model. For this project, we plan to first generalize this domain decomposition method to the polarizable continuum model with anisotropic dielectrics and compare it with the other existing equivalent methods through numerical experiments. Then, in the simplest case of conductor-like screening model, we aim to prove theoretically its convergence which has been observed numerically. Finally, for the linearized Poisson-Boltzmann solvation model, we want to apply this method in the molecular dynamics to obtain a better simulation.