Parallel Adaptive Lagrangian Discontinuous Galerkin Simulation of Pediatric Brain Injury

这项工作的总体目标是开发计算工具，以更好地研究“摇晃婴儿综合症”。该项目将发展高精度的并行自适应拉格朗日间断伽辽金技术，用于流体力学和固体力学的模拟。这些技术将是开发高保真模拟工具的核心，用于研究儿童脑损伤机制和预防策略。即使是当今使用最好的代码的最强大的计算机也需要几周或几个月的时间来进行这些计算。此外，由于使用的低阶(O(H))有限元/有限差分格式和显式时间积分格式(O(Dt))的数值精度较低，即使是这些大胆的计算也不能提供合理的模拟。新策略的关键是开发和使用并行自适应hp Lagrangian间断Galerkin格式，这些格式提供了处理脑组织、相关膜和血管的复杂几何和材料结构所需的精度和效率。这些方案将允许使用高阶近似来获得对p，k 1的O(Hp)和O(Dtk)的精度。虽然儿科脑损伤的应用将推动对这类新的并行计算技术的研究，但这些代码和方法应该对更广泛的问题类别有用。

The overall goal of this work is to develop the computational tools to better study "shaken baby syndrome". This project will develop highly accurate parallel adaptive Lagrangian discontinuous Galerkin techniques for the simulation of fluid mechanics and solid mechanics. These techniques will be central to the development of high fidelity simulation tools for investigation of pediatric brain injury mechanisms and preventative strategies. Even the most powerful computers today using the best available codes would need weeks or months to do these calculations. Moreover, even those heroic calculations would not provide reasonable simulations due to the poor numerical accuracy of the lower order (O(h)) finite element / finite difference schemes and explicit time integration schemes (O(Dt)) used.The key element of the new strategy is the development and use of parallel adaptive hp Lagrangian discontinuous Galerkin schemes that provide the accuracy and efficiency necessary for dealing with the complex geometric and material structure of the brain tissue, associated membranes, and blood vessels. These schemes will enable the use of higher order approximations to obtain accuracies that are O(hp) and O(Dtk), for p, k 1. While the pediatric brain injury application will drive the research into this new class of parallel computational techniques, the codes and methodology should be useful for a much wider class of problems.