Research Initiation: Solution Refinement by the Adaptive Mesh Superposition Method

计算力学的主要挑战之一是 解析结构的数值方法的发展 在复杂的几何形状中具有高梯度的函数。 在 由于局部化和裂纹导致的材料失效等问题 传播，或冲击在流体动力学，高的区域 梯度的数量级小于 关注领域的大小。 因此，如果一个统一的有限 元素网格，大量的元素 将需要准确地解决结构的高 梯度。 本研究的目的是为了提高有限差分法的质量， 高梯度区域的元素计算。 这是 通过叠加一片高阶的 原始有限域上的层次元素 需要分辨率的单元网格。 的连续性 位移场是通过施加均匀的 原始场和叠加场之间的边界。 的 叠加和原始网格拓扑。 研究 作为该项目的一部分，将考虑 以下方面： 1. 制定和执行 有限元网格叠加法 2. 叠加法的自动化。 高分辨率的字段将获得通过控制 叠加场的位置、其细分和 叠加元素的多项式阶。 过程 这些变量的选择将由后验 信息. 逐点误差和叠加网格将 设计为几乎最佳地利用后部 信息.

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.