Research Initiation: Solution Refinement by the Adaptive Mesh Superposition Method

研究启动：通过自适应网格叠加方法细化解

基本信息

批准号：
9003093
负责人：
Jacob Fish
金额：
$ 6.6万
依托单位：
Rensselaer Polytechnic Institute
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1990
资助国家：
美国
起止时间：
1990-06-15 至 1992-11-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9003093&HistoricalAwards=false
关键词：
Research Initiation Solution Refinement Adaptive

项目摘要

One of the major challenges in computational mechanics is the development of numerical methods for resolving the structure of functions with high gradients in complicated geometries. In problems such as material failure due to localization and crack propagation, or shocks in fluid dynamics, the regions of high gradients are of several orders of magnitude smaller than the size of the domain of interest. Therefore, if a uniform finite element mesh is used, a tremendous amount of elements would be needed to accurately resolve the structure of high gradients. The purpose of this research is to improve the quality of finite element calculations in the regions of high gradients. This is accomplished by superimposing a patch of higher order hierarchical elements on the portion of the original finite element mesh where resolution is required. Continuity of the displacement field is maintained by imposing homogenous boundaries between the original and superimposed fields. The superimposed and the original mesh topology. The research to be carried out as part of this project will consider the following aspects: 1. The development and implementation of the finite element mesh superposition method. 2. Automation of the superposition method. High resolution of the fields will be obtained by controlling the location of the superimposed field, its subdivision and the polynomial order of the superimposed elements. The process of selection of these variables will be steered by a posteriori information. Pointwise error and the superimposed mesh will be designed to make a nearly optimal use of posterior information.

计算力学的主要挑战之一是开发解决复杂几何中高梯度函数结构的数值方法。在诸如由于局部化和裂纹扩展导致的材料失效或流体动力学冲击等问题中，高梯度区域比感兴趣区域的尺寸小几个数量级。因此，如果使用统一的有限元网格，则需要大量的单元来精确解析高梯度的结构。本研究的目的是提高高梯度区域有限元计算的质量。这是通过在原始有限元网格中需要分辨率的部分上叠加一片高阶分层元素来实现的。通过在原始场和叠加场之间施加均匀边界来保持位移场的连续性。叠加的和原始的网格拓扑。作为该项目的一部分，将进行的研究将考虑以下几个方面： 1.有限元网格叠加方法的开发和实现。 2.叠加方法的自动化。通过控制叠加场的位置、细分以及叠加元素的多项式阶数，可以获得高分辨率的场。这些变量的选择过程将由后验信息引导。点误差和叠加网格将被设计为近乎最佳地利用后验信息。