Next-generation methods for transport in poroelastic media with interfaces

可变形多孔结构在诸如过滤器、海绵和假体的材料设计中是普遍存在的。它们往往表现出复杂的机械化学过程，发生在几个时空尺度。数学上描述它们需要耦合的非线性、多物理和多尺度方程组。这使得精确、高效的数值方法的设计具有挑战性。该奖学金的目的是解决在poromechanics方程及其离散化方法中遇到的数学特性，并设计新的数学和计算技术，用于将分析扩展到大变形和存在界面以及与其他相邻元素耦合的情况。

Deformable porous structures are ubiquitous in the design of materials such as filters, sponges, and prosthetics. They often show complex mechano-chemical processes that occur across several spatio-temporal scales. To mathematically describe them requires coupled sets of nonlinear, multiphysical, and multiscale equations. This makes the design of accurate, efficient numerical methods challenging. The Fellowship aims to address the mathematical characteristics encountered in poromechanics equations and their discretisation methods, and to devise novel mathematical and computational techniques for extending the analysis to cases where large deformations and the presence of interfaces and coupling with other neighbouring elements are relevant.