Advanced mathematical modelling and computation of fractional sub-diffusion problems in complex domains

在过去的几十年里，研究人员已经观察到许多生物，物理和金融系统，其中一些关键的潜在随机运动不符合经典的扩散模型。该项目将通过正确地纳入非线性反应、强迫和不规则几何形状的混杂效应，扩展目前描述这种异常亚扩散的宏观模型。该项目的一个关键方面是新算法的设计，这将从根本上提高直接数值模拟的精度和效率的子扩散在具有挑战性的应用。

Over the past few decades, researchers have observed numerous biological, physical and financial systems in which some key underlying random motion fails to conform to the classical model of diffusion. The project will extend current macroscopic models describing such anomalous sub-diffusion by correctly incorporating the confounding effects of nonlinear reactions, forcing and irregular geometry. A key aspect of the project is the design of new algorithms that will fundamentally improve the accuracy and efficiency of direct numerical simulations of sub-diffusion in challenging applications.