Kohn-Sham模型的自适应有限元逼近
Adaptive Finite Element Approximations for Kohn-Sham Models
AI总结：
针对Kohn-Sham模型，提出基于残差的后验误差估计器，设计自适应有限元算法并证明收敛性，通过Dörfler标记策略获得收敛速率和拟最优复杂度，数值实验验证了方法的鲁棒性和效率。
摘要：
Kohn-Sham方程是化学、材料科学、生物学和纳米科学中计算基态电子能量和密度的强大且广泛使用的方法。本文研究了Kohn-Sham模型的自适应有限元逼近。基于本文提出的残差型后验误差估计器，我们引入了一种具有相当一般标记策略的自适应有限元算法，并证明了自适应有限元逼近的收敛性。使用Dörfler标记策略，我们进一步得到了收敛速率和拟最优复杂度。我们还进行了几个典型的数值实验，不仅支持了我们的理论，而且展示了自适应有限元计算在电子结构计算中的鲁棒性和效率。
英文摘要：
The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences. In this paper, we study the adaptive finite element approximations for the Kohn-Sham model. Based on the residual type a posteriori error estimators proposed in this paper, we introduce an adaptive finite element algorithm with a quite general marking strategy and prove the convergence of the adaptive finite element approximations. Using D{\" o}rfler's marking strategy, we then get the convergence rate and quasi-optimal complexity. We also carry out several typical numerical experiments that not only support our theory,but also show the robustness and efficiency of the adaptive finite element computations in electronic structure calculations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
