Reduced over collocation based on residual hyper reduction for steady state and time-dependent nonlinear equations

：纪丽洁（上海大学）
：2024-11-07 16:00
：海韵园实验楼106报告厅

报告人：纪丽洁（上海大学）

时  间：2024年11月7日16:00

地  点：海韵园实验楼106报告厅

内容摘要:

The need for multiple interactive, real-time simulations using different parameter values has driven the design of fast numerical algorithms with certifiable accuracies. The reduced basis method (RBM) presents itself as such an option. RBM features a mathematically rigorous error estimator which drives the construction of a low-dimensional subspace. A surrogate solution is then sought in this low-dimensional space approximating the parameter-induced high fidelity solution manifold. However, when the PDE is nonlinear or its parameter dependence nonaffine, the empirical interpolation method (EIM) will be involved for further reduction. In our work, we augment and extend the EIM approach as a direct solver, as opposed to an assistant, for solving nonlinear pPDEs on the reduced level. Two critical ingredients of the scheme are collocation at about twice as many locations as the number of basis elements for the reduced approximation space, and an efficient error indicator for the strategic building of the reduced solution space. Numerical tests on different families of time-dependent and steady-state nonlinear problems demonstrate the high efficiency and accuracy of our R2-ROC and its superior stability performance.

个人简介：

纪丽洁，上海大学数学系讲师。2021年博士毕业于上海交通大学。2019年至2020年在马萨诸塞大学达特茅斯分校访学一年。2021年至2023年，在上海交通大学博士后流动站从事博士后研究。主要研究方向为电荷输运问题的理论和数值分析、参数化偏微分方程的模型降阶算法、等离子体物理的数值算法以及黑盒优化问题等。在SIAM J. Appl. Math., SIAM J. Sci. Comput. , J. Comput. Phys.，J. Sci. Comput.等期刊发表论文。获得2021年上海市超级博士后奖励计划资助，主持过中国博士后科学基金面上资助1项，现主持国家自然科学基金青年基金1项，上海大学-青年英才启航计划1项。

 

联系人：赵状