Autonomous Control of Mesh Adaptations for the Discontinuous Galerkin Method Applied to Problems in Electrodynamics

应用于电动力学问题的间断伽辽金法网格自适应的自主控制

• 批准号: 174570894
• 负责人: Professor Dr.-Ing. Thomas Weiland
• 金额: --
• 依托单位: Institut für Teilchenbeschleunigung und Elektromagnetische Felder
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/174570894?language=en
• 关键词: Autonomous; Control; Mesh; Adaptations; Discontinuous

The Discontinuous Galerkin Method (DG) is a high order numerical Method, which attracted considerable attention in recent years. Within the DG method the approximation order can be chosen locally on the element level. As computational costs rise alongside with the approximation order the application of adaptive methods allowing for controlling accuracy based on the local error should be considered in order to reach a given error tolerance with the minimal number of degrees of freedom. As the Discontinuous Galerkin Method is a Finite Element Method two options for local adaptation are available, i.e., the adaptation of the local mesh step size and the local approximation order. During the first two years of this project (already funded by the DFG) new, autonomous mesh controls as well as new error estimators have been developed and compared. In the second phase we wish to complete the extension of the method to a space-time scheme. This will allow for adaptively controlling errors also along the time dimension leading to a scheme, which can reach a prescribed error tolerance in space and time at minimal computational costs.

间断伽辽金法是近年来引起人们广泛关注的一种高阶数值方法。在DG方法中，近似阶可以在元素级上局部选择。随着计算成本随着近似阶数的增加而增加，应考虑应用允许基于局部误差控制精度的自适应方法，以便以最小的自由度达到给定的误差容限。由于不连续Galerkin方法是有限元方法，所以局部自适应的两个选项是可用的，即，局部网格步长和局部逼近阶的自适应。在该项目的前两年（已经由DFG资助），新的，自主的网格控制以及新的误差估计器已经开发和比较。在第二阶段，我们希望完成的方法扩展到一个空间-时间计划。这将允许也沿沿着时间维度自适应地控制误差，从而产生能够以最小计算成本在空间和时间上达到规定的误差容限的方案。