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

EAGER 提案：3D x 时间的自适应时空不连续伽辽金方法

• 批准号: 0948393
• 负责人: Robert Haber
• 金额: $ 20万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0948393&HistoricalAwards=false
• 关键词: EAGER; Proposal; Adaptive; Spacetime; Discontinuous

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.

该奖项根据 2009 年美国复苏和再投资法案（公法 111-5）提供资金。时空不连续伽辽金 (SDG) 方法是一种新的计算技术，其新颖的数学框架所产生的算法在需要对偏微分方程组和常微分方程组进行高分辨率解的各种应用学科中具有潜在的重大影响。这里提出的探索性研究计划将证明将 SDG 方法扩展到通用数值框架的可行性，用于求解最多 3D ×时间的任意类型的偏微分方程组。该技术将基于独特的自适应时空网格划分，建立在经典离散哈密顿动力学理论的基础上，形成真正的场理论。项目还将引入一种用于逼近抛物线系统的新的多尺度双曲松弛，以及一种基于 hp 自适应、基于因果关系的守恒定律建模方法，该方法不需要超出基本 SDG Galerkin 投影的数值稳​​定性。