论文标题
离散的经验插值和未固定网格FEM：在PDE受限优化中的应用
Discrete Empirical Interpolation and unfitted mesh FEMs: application in PDE-constrained optimization
论文作者
论文摘要
在这项工作中，我们研究了性能CUTFEM作为高保真求解器，以及我们在固定背景几何和网格中构建了一个有能力且经济的订购求解器，以用于PDE受限的优化域中。它的有效性和可靠性将通过其应用于用椭圆方程作为约束的二次优化问题的数值解决方案进行评估，从而检查原型情况。减少策略将通过使用汇总状态和伴随测试空间的适当正交分解，而离线连接解耦的效率将通过离散的经验插值来确保最佳系统矩阵和右侧的经验插值，从而快速解决每种新的订单模型的快速分辨率。
In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed background geometry and mesh. Its effectiveness and reliability will be assessed through its application for the numerical solution of quadratic optimization problems with elliptic equations as constraints, examining an archetypal case. The reduction strategy will be via Proper Orthogonal Decomposition of suitable FE snapshots, using an aggregated state and adjoint test space, while the efficiency of the offline-online decoupling will be ensured by means of Discrete Empirical Interpolation of the optimality system matrix and right-hand side, enabling thus a rapid resolution of the reduced order model for each new spatial configuration.
