EAGER Proposal: Adaptive Spacetime Discontinuous Galerkin Methods in 3D x time

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。时空不连续伽辽金（SDG）方法是一种新的计算技术，其新颖的数学框架导致了具有重大意义的算法。在需要高分辨率解的偏微分方程和常微分方程系统的各种应用学科中都不能产生影响。这里提出的探索性研究计划将证明将可持续发展目标方法扩展到一个通用数值框架的可行性，该框架可用于求解任意类型的pde系统，直至3D ×time。该技术将基于独特的自适应时空网格，建立在经典的离散哈密顿动力学理论的基础上，以实现真正的古人的理论。该项目还将引入一种新的多尺度双曲松弛法，用于近似抛物线系统，以及一种基于hp自适应、基于因果关系的方法来建模守恒定律，该方法不需要超出基本SDG Galerkin投影的数值稳定。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The spacetime discontinuous Galerkin (SDG) method is a new computational technology whose novel mathematical framework leads to algorithms that have the potential for significant impact in a wide variety of application disciplines wherever high-resolution solutions to systems of partial and ordinary differential equations are required. The exploratory research program proposed here would demonstrate the feasibility of extending the SDG methodology to a general-purpose numerical framework for solving systems of PDEs of arbitrary type in up to 3D ×time. The technology will be based on unique adaptive spacetime meshing, building up on the classical discrete Hamiltonian dynamics theory to a true field theory. Project will also introduce a new multi-scale hyperbolic relaxation for approximating parabolic systems, and an hp-adaptive, causality-based approach to modeling conservation laws that requires no numerical stabilization beyond the basic SDG Galerkin projection.