11月21日 徐岩教授学术报告

发布时间:2025-11-17

报告题目：A kernel compensation mimetic finite difference scheme for eigenvalue problem

主讲人：徐  岩教授，中国科学技术大学 

报告时间：2025年11月21日（周五），14:00-15:00

报告地点：计算机学院A501

主持人：邹青松教授

摘要：

We propose a kernel compensation type mimetic finite difference (MFD) scheme aimed at solving the grad-div eigenvalue problem. This method utilizes a curl-curl type compensation operator along with carefully selected boundary conditions to effectively manage the infinite-dimensional kernel of the grad-div operator. To ensure high accuracy, we apply stencil-based mimetic finite difference operators to discretize the grad-div operator under Dirichlet boundary conditions. This results in a numerical scheme characterized by a sparse stiff matrix with a narrow bandwidth while achieving high-order accuracy.  We construct the compensation operator with a proper boundary condition that is orthogonal with the discrete grad-div operator. Generalized identify method for spurious eigenvalues are presented. The resulting scheme offers several advantages, including high-order accuracy, enhanced computational efficiency with reduced memory usage, and excellent scalability for parallel computation.  Numerical tests demonstrate that our approach not only converges at the expected rates but also performs satisfactorily in terms of speed.

主讲人简介：

徐岩，中国科学技术大学数学科学学院教授、博导，教育部国家重大人才工程项目特聘教授，国家自然科学基金优秀青年基金、教育部新世纪优秀人才计划、中国数学会计算数学分会第二届“青年创新奖”获得者。主要研究领域为高精度数值计算方法。担任SIAM Journal on Scientific Computing, Journal of Scientific Computing, Advances in Applied Mathematics and Mechanics, Communication on Applied Mathematics and Computation、计算物理等杂志的编委。