Next-generation methods for transport in poroelastic media with interfaces

在过滤器、海绵和假肢等材料的设计中，可变形的多孔结构是普遍存在的。它们常常表现出发生在几个时空尺度上的复杂的机械力-化学过程。要从数学上描述它们，需要一组耦合的非线性、多物理和多尺度方程。这使得设计准确、高效的数值方法具有挑战性。该奖学金的目的是解决孔洞力学方程及其离散化方法中遇到的数学特征，并设计新的数学和计算技术，以将分析扩展到大变形和存在界面以及与其他相邻单元的耦合的情况。

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.