论文标题
非局部静电的Trefftz功能
Trefftz Functions for Nonlocal Electrostatics
论文作者
论文摘要
溶剂中的静电相互作用在生物物理系统中起主要作用。文献中有一个共识，即水溶液的介电响应是非本地的：极化不仅取决于给定点的电场，而且还取决于该点附近的电场。这通常是通过电场的卷积与适当的积分内核进行建模。 非本地模型的主要问题是高计算成本。次要问题是将卷积积分限制为溶剂，而不是在整个空间中的评估。 本文开发了一种计算工具，以减轻“非局部性的诅咒”并有助于正确处理集成。该工具是trefftz近似值，它倾向于比传统多项式的近似值更高。在本文中，针对非局部静电的问题开发了TREFFTZ近似值，其目的是“定位”原始的非局部问题。在计算数学，物理和工程学的其他领域，这种方法可以扩展到非局部问题。
Electrostatic interactions in solvents play a major role in biophysical systems. There is a consensus in the literature that the dielectric response of aqueous solutions is nonlocal: polarization depends on the electric field not only at a given point but in the vicinity of that point as well. This is typically modeled via a convolution of the electric field with an appropriate integral kernel. A primary problem with nonlocal models is high computational cost. A secondary problem is restriction of convolution integrals to the solvent, as opposed to their evaluation over the whole space. The paper develops a computational tool alleviating the "curse of nonlocality" and helping to handle the integration correctly. This tool is Trefftz approximations, which tend to furnish much higher accuracy than traditional polynomial ones. In the paper, Trefftz approximations are developed for problems of nonlocal electrostatics, with the goal of numerically "localizing" the original nonlocal problem. This approach can be extended to nonlocal problems in other areas of computational mathematics, physics and engineering.
