Numerical approximation of high-dimensional Fokker-Planck equations (C08)

高维福克-普朗克方程的数值逼近（C08）

• 批准号: 438916983
• 金额: --
• 依托单位: Institut für Geometrie und Praktische Mathematik (IGPM)
• 依托单位国家: 德国
• 项目类别: CRC/Transregios
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/438916983?language=en
• 关键词: Numerical; approximation; dimensional; Fokker; Planck

The goal of this project is the development of numerical methods for the error-controlled approximation of Fokker-Planck equations in high dimensions, with particular focus on equations describing dilute polymer solutions and solutions with active particles. Two different classes of approximations are considered: sparse product basis expansions parameterized by low-rank tensor decompositions, and approximations by sums of high-dimensional Gaussian functions.

该项目的目标是开发用于高维度福克-普朗克方程的误差控制近似的数值方法，特别关注描述稀聚合物溶液和具有活性粒子的溶液的方程。两种不同的类的近似被认为是：稀疏的产品的基础上展开参数化的低秩张量分解，和近似的高维高斯函数的总和。