Speaker: Xu Yan, Professor and Doctoral Supervisor, University of Science and Technology of China

Date: December 19, 2025

Time: 15:30-16:30 pm

Location: B936, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

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.

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https://www.view.sdu.edu.cn/info/1020/208646.htm