Multiresolution numerical methods for the integral equation theory of solute-solvent interactions in molecular liquids

分子液体积分方程式理论已被证明是计算流体中分子体系结构和热力学性质的有力工具。然而，即使对于单原子溶质浸入分子液体的最简单情况，该理论也需要Ornstein-Zernike型积分方程组的非平凡数值解。随着溶质和模型液体相互作用分子位数目的增加，溶液的复杂性急剧增加。这就是为什么该理论仍远未成为模拟凝聚分子系统的“行业工具”，主要是因为缺乏有效的算法和可用的数值库。该方案的主要目的是利用现代计算数学方法，如非线性方程的多分辨小波逼近和多重网格法，为分子液体中溶质-溶剂相互作用的积分方程组理论开发一个有效的计算工具。我们计划提供一系列数值库，这些库可用于理论的广泛应用领域，从简单的单原子溶质到水溶液中的生物分子和超分子组装。

The integral equation theory of molecular liquids has been proven to be a powerful tool for the calculation of both structural and thermodynamical properties of molecular systems in fluids. However, even for the simplest case of a monoatomic solute immersed in a molecular liquid the theory requires a non-trivial numerical solution of a system of integral equations of the Ornstein-Zernike type. The complexity of solution dramatically increases with the increasing number of interacting molecular sites of the solute and the model liquid. That is why the theory is still far from being 'tool of the trade' for modelling condensed molecular systems, mainly, because of the lack of efficient algorithms and numerical libraries available. The main objective of the proposal is to develop an efficient computational tool for the integral equation theory of solute-solvent interactions in molecular liquids using the modern methods of computational mathematics such as multiresolution wavelet approximation and multi-grid methods for nonlinear equations. We plan to deliver a collection of numerical libraries which can be used for a wide area of applications of the theory from simple monoatomic solutes to biomolecules and supramolecular assemblies in aqueous solutions.