A kernel compensation mimetic difference scheme for the grad-div eigenvalue problem

doi:10.1016/j.camwa.2025.11.015

A kernel compensation mimetic difference scheme for the grad-div eigenvalue problem

2025-12-04

0

PRE

AI

DOI：10.1016/j.camwa.2025.11.015

Original

Original request for help

Save

Abstract

En 中文

We propose a kernel compensation mimetic difference (MD) scheme to solve 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 MD 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 to the discrete grad-div operator. A generalized identification method for spurious eigenvalues is 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.

A kernel compensation mimetic difference scheme for the grad-div eigenvalue problem

Abstract

Journal

Organization