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March 26, 2025Inverse Problems

A mixed finite element scheme for three-dimensional Maxwell’s transmission eigenvalue problems

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Authors

QLQing LiuHuanggang Normal University TLTiexiang LiShanghai Institute for Mathematics and Interdisciplinary Sciences WLWen-Wei LinShanghai Institute for Mathematics and Interdisciplinary Sciences

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Implication

Computational study demonstrates an efficient mixed finite element method for Maxwell transmission eigenvalue problems, indicating optimal convergence without spurious eigenvalues.

Key Points

Develop an accurate and efficient numerical solver for three-dimensional Maxwell's transmission eigenvalue problems on domains with a vanishing first Betti number.
Reduced the fourth-order formulation to an equivalent stable linear eigenvalue problem with a compact operator using auxiliary variables.
Discretized the formulation using a mixed finite element scheme to yield a sparse generalized eigenvalue problem (GEP).
Deflated infinite eigenvalues while preserving sparse matrix structures and applied a multigrid-type block Jacobi–Davidson method to compute the smallest positive real eigenvalues.
Achieved optimal theoretical convergence rates for calculated eigenvalues without introducing spurious eigenvalues.
Maintained sparse matrix multiplication efficiency during preprocessing and demonstrated robust numerical performance across three-dimensional benchmarks.

Cite This Study

Liu et al. (2025) studied this question.

synapsesocial.com/papers/6a838693daf812a7fbcd7c63 https://doi.org/10.1088/1361-6420/adc597

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Implication

Computational study demonstrates an efficient mixed finite element method for Maxwell transmission eigenvalue problems, indicating optimal convergence without spurious eigenvalues.

A mixed finite element scheme for three-dimensional Maxwell’s transmission eigenvalue problems

Discussion

Member takes

Implication

Key Points

Cite This Study

A mixed finite element scheme for three-dimensional Maxwell’s transmission eigenvalue problems

Discussion

Member takes

Implication

Key Points

Cite This Study

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