Towards predictive 4D computational models for the heart

该项目旨在为具有动态界面的多尺度和多物理PDE开发新的高性能数值算法，开发和分析模拟心脏和躯干机电的新型PDE系统，并将这些数值技术和模型相结合，为患者特定的心脏功能模拟提供预测工具。它涉及嵌入网格上的时空变分离散的设计和数学分析，用于数值积分的四维计算几何算法和多层解算器。通过结合科学计算和机器学习，这项研究的一个预期结果是新一代非线性偏微分方程近似和求解器。

This project aims to develop novel high-performance numerical algorithms for multiscale and multiphysics PDEs with dynamic interfaces, the development and analysis of a novel PDE system modelling the electromechanics of heart and torso, and the combination of these numerical techniques and models to deliver predictive tools for patient-specific simulations of the cardiac function. It involves the design and mathematical analysis of space-time variational discretisations on embedded meshes, 4D computational geometry algorithms for numerical integration and multilevel solvers. By combining scientific computing and machine learning, one anticipated outcome of this research is a new generation of nonlinear PDE approximations and solvers.