In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive procedure is driven by two residual type a posteriori error estimators, one for the state variable and the other for the objective functional. The adaptive algorithm is provably convergent in the sense that the sequence of numerical approximations generated by the adaptive algorithm contains a subsequence convergent to a solution of the continuous first-order optimality system. We provide several numerical simulations to show the distinct features of the algorithm.

翻译：本文提出了一种自适应算法，用于高效数值求解拓扑优化中的最小柔度问题。该算法采用相场近似和连续密度场。自适应过程由两个残差型后验误差估计器驱动：一个针对状态变量，另一个针对目标泛函。该自适应算法具有可证明的收敛性，即由该算法生成的数值逼近序列包含一个收敛到连续一阶最优性系统解的子序列。我们通过若干数值模拟展示了该算法的显著特征。