Goal-oriented r-adaptivity based on variational arguments in the physical and material spaces
Goal-oriented r-adaptivity based on variational arguments in the physical and material spaces
复制标题
基于物理和物质空间中变分参数的目标导向的 r 适应性
DOI：
10.1016/j.cma.2009.06.015
复制
发表时间：
2009
影响因子：
7.2
通讯作者：
F. Barthold
中科院分区：
文献类型：
--
作者：
D. Materna;F. Barthold
局部感兴趣量的误差取决于相应的对偶解或广义绿色函数的误差。这一事实被用于基于双加权的面向目标的误差估计技术和h-或p-自适应算法。这一贡献是关于一种新的方法，以目标为导向的r-适应性的基础上能源最小化原则的原始和对偶问题。原始问题的能量最小化以及对偶问题的能量最小化相对于设计函数分别导致原始和对偶材料残差。这些残差是当前网格上离散化误差的误差指示器。我们提出了一个面向目标的网格优化算法，它结束在一个优化的网格相对于所选择的感兴趣的数量。通过选定的计算实例，我们证明了所提出的框架的能力。
The error in a local quantity of interest depends on the error in the corresponding dual solution or generalized Green’s function. This fact is used in dual-weighted based goal-oriented error estimation techniques and h- or p-adaptive algorithms. This contribution is concerned with a novel approach for goal-oriented r-adaptivity based on energy minimization principles for the primal and the dual problems. The minimization of the energy of the primal problem as well as the minimization of the energy of the dual problem with respect to a design function lead to the primal and dual material residuals, respectively. These residuals are error indicators for the discretization error on the current mesh. We propose a goal-oriented mesh optimization algorithm which ends in an optimized mesh with respect to a chosen quantity of interest. By means of selected computational examples, we demonstrate the capability of the proposed framework.