RIA: An Adaptive Spectral Element Method for the Solution ofTransient Partial Differential Equations in Complex Geometries

本研究的主要目的 启动项目要素 求解时间的算法 相依偏微分 模拟物理的方程 复杂几何中的现象。 自适应方法将确保 计算机优化配置 存储方面的资源， CPU时间通过自动细化， 粗化或重建 用于离散化的几何网格 空间中的方程 计算。该方法将是 以一种普遍的方式发展， 创新将是独立的， 几何学和方程式的 模拟. 这种方法将 使许多领域受益， 高阶应用 光谱方法可用于 复杂物理模拟 现象。 主要任务是建设 基于规则的系统， 完善，发展一个 动态分配方案 用于改变网格的空间 连接信息， 网格优化的发展 标准，确保网格 修改是时间精确的， 保守并最终改进 当前误差估计器和 预处理器研究 需要理论和 计算工作，并将包括 一些测试和小说 仿真。 的自适应公式化 谱元法是针对 增加了灵活性， 高阶能力范围 方法一般。 高阶 方法提供高度准确的 模拟速度非常快， 收敛，通常用于 在直接模拟基本 物理现象。 拟议 研究将允许高阶 处理“真实的”的方法 工程问题，而不是 理想化的研究问题， 减少所需的计算机 一至两个数量级的 magnitude.//

The main objective of this research initiation project (RIA) element algorithm for the solution of time dependent partial differential equations to simulate physical phenomena in complex geometries. The adaptive method will ensure optimal allocation of computer resources in terms of storage and cpu time by automatically refining, coarsening or reconstructing the geometric mesh used to discretize the equations in space throughout the calculation. The method wil be developed ina general way, in that the innovations will be independent of the geometry and equations to be simulated. This approach will benefit the many fields in which the application of high order spectral methods can be used for simulation of complex physical phenomena. THe main tasks are the construction of a rule-based system for refinement, the development of a scheme for dynamic allocation of space for the changing mesh connectivity information, the development of a mesh optimization criterion, ensuring that the mesh alteration is time-accurate and conservative and finally improving the current error estimators and preconditioners. The research entails theoretical and computational work and will include a number of test and novel simulations. The adaptive formulation of the spectral element method is aimed at increasing the flexibility and range of capabilities of high order methods in general. High order methods provide highly accurate simulations with very fast rates of convergence and are typically used in the direct simulation of basic physical phenomena. The proposed research will allow high order methods to deal with "real" engineering problems, rather than idealized research problems, by reducing the needed computer resources by one to two orders of magnitude.//