报告题目：A low-rank approximation method for linear elasticity with random interfaces

报告人：郝永乐 周口师范学院数学与统计学院

报告时间：2025年11月29日 下午14:40-15:20

报告地点：#腾讯会议：740254516

校内联系人：张剑桥 [email protected]

报告摘要：In this talk, we presents a computational framework for linear elasticity problems with random interfaces. By integrating shape calculus, low-rank approximation, and weak Galerkin finite element method, the framework efficiently quantifies solution statistics. We first provide a rigorous characterization of random interfaces under C^{2,1}-regularity and derive the governing equations for shape derivatives. A novel hybrid algorithm is then proposed, combining weak Galerkin method with a pivoted Cholesky decomposition to achieve superior computational efficiency in variance estimation over conventional Monte Carlo methods at equivalent accuracy. We rigorously derive a priori error estimates, establishing discretization errors of order O(h^2), random errors in expectation of order O(\delta^2), and in variance of order O(\delta^3). Numerical experiments in R^d (d = 2,3) confirm the method’s effectiveness and robustness.

报告人简介：郝永乐, 博士, 周口师范学院数学与统计学院副教授，研究方向：偏微分方程数值解。发表论文14篇，发表学术专著1部，参编教材2部。主持国家自然基金青年基金、河南省高等学校重点项目，参与国家自然基金青年基金、河南省科技攻关项目等。