A Holomorphic Operator Function Approach for the Modified Transmission Eigenvalue Problem

Huaijia Zhang; Xia Ji

doi:10.4208/cicp.OA-2025-0075

A Holomorphic Operator Function Approach for the Modified Transmission Eigenvalue Problem

Huaijia Zhang
, Xia Ji^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology
Shenzhen MSU-BIT University

Research output: Contribution to journal › Article › peer-review

Abstract

The paper presents a holomorphic operator function approach for solving the modified transmission eigenvalue problem using the finite element method. To use the abstract approximation theory for holomorphic operator functions, we rewrite the modified transmission eigenvalue problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence of the finite element method is proved following the abstract theory of the holomorphic Fredholm operator function. Numerical examples are presented to validate the theory.

Original language	English
Pages (from-to)	762-780
Number of pages	19
Journal	Communications in Computational Physics
Volume	40
Issue number	3
DOIs	https://doi.org/10.4208/cicp.OA-2025-0075
Publication status	Published - 31 May 2026

Keywords

Finite element method
Fredholm operator
modified transmission eigenvalue problem

Access to Document

10.4208/cicp.OA-2025-0075

Cite this

@article{8b18ad26d38f4da3a39f32f5d94297e9,

title = "A Holomorphic Operator Function Approach for the Modified Transmission Eigenvalue Problem",

abstract = "The paper presents a holomorphic operator function approach for solving the modified transmission eigenvalue problem using the finite element method. To use the abstract approximation theory for holomorphic operator functions, we rewrite the modified transmission eigenvalue problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence of the finite element method is proved following the abstract theory of the holomorphic Fredholm operator function. Numerical examples are presented to validate the theory.",

keywords = "Finite element method, Fredholm operator, modified transmission eigenvalue problem",

author = "Huaijia Zhang and Xia Ji",

note = "Publisher Copyright: {\textcopyright}2026 Global-Science Press",

year = "2026",

month = may,

day = "31",

doi = "10.4208/cicp.OA-2025-0075",

language = "English",

volume = "40",

pages = "762--780",

journal = "Communications in Computational Physics",

issn = "1815-2406",

publisher = "Global Science Press",

number = "3",

}

TY - JOUR

T1 - A Holomorphic Operator Function Approach for the Modified Transmission Eigenvalue Problem

AU - Zhang, Huaijia

AU - Ji, Xia

PY - 2026/5/31

Y1 - 2026/5/31

N2 - The paper presents a holomorphic operator function approach for solving the modified transmission eigenvalue problem using the finite element method. To use the abstract approximation theory for holomorphic operator functions, we rewrite the modified transmission eigenvalue problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence of the finite element method is proved following the abstract theory of the holomorphic Fredholm operator function. Numerical examples are presented to validate the theory.

AB - The paper presents a holomorphic operator function approach for solving the modified transmission eigenvalue problem using the finite element method. To use the abstract approximation theory for holomorphic operator functions, we rewrite the modified transmission eigenvalue problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence of the finite element method is proved following the abstract theory of the holomorphic Fredholm operator function. Numerical examples are presented to validate the theory.

KW - Finite element method

KW - Fredholm operator

KW - modified transmission eigenvalue problem

UR - https://www.scopus.com/pages/publications/105040358576

U2 - 10.4208/cicp.OA-2025-0075

DO - 10.4208/cicp.OA-2025-0075

M3 - Article

AN - SCOPUS:105040358576

SN - 1815-2406

VL - 40

SP - 762

EP - 780

JO - Communications in Computational Physics

JF - Communications in Computational Physics

IS - 3

ER -

A Holomorphic Operator Function Approach for the Modified Transmission Eigenvalue Problem

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this