A Multi-level Mixed Element scheme of the two dimensional helmholtz transmission eigenvalue problem

2017/07/03 by Xi Yu, Xi, Y., Xia Ji +3
Engineering · Mathematics · #47B07 #65N25 #65N30 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1707.00567

openalex publication_date 2017/07/03 · openalex created_date 2017/07/14 · openalex updated_date 2026/07/28

Abstract

In this paper, we present a multi-level mixed element scheme for the Helmholtz transmission eigenvalue problem on polygonal domains that are not necessarily able to be covered by rectangle grids. We first construct an equivalent linear mixed formulation of the transmission eigenvalue problem and then discretize it with Lagrangian finite elements of low regularities. The proposed scheme admits a natural nested discretization, based on which we construct a multi-level scheme. Optimal convergence rate and optimal com- putational cost can be obtained with the scheme.

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