In this paper,we develop the stabilization-free virtual element method for the Helmholtz transmission eigenvalue problem on anisotropic media.The eigenvalue problem is a variable-coefficient,non-elliptic,non-selfadjoi...In this paper,we develop the stabilization-free virtual element method for the Helmholtz transmission eigenvalue problem on anisotropic media.The eigenvalue problem is a variable-coefficient,non-elliptic,non-selfadjoint and nonlinear model.Separating the cases of the index of refraction n≠1 and n≡1,the stabilization-free virtual element schemes are proposed,respectively.Furthermore,we prove the spectral approximation property and error estimates in a unified theoretical framework.Finally,a series of numerical examples are provided to verify the theoretical results,show the benefits of the stabilization-free virtual element method applied to eigenvalue problems,and implement the extensions to high-order and high-dimensional cases.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12301532,12271523,12071481,12371198,12371374)by the Defense Science Foundation of China(Grant Nos.2021-JCJQ-JJ-0538,2022-JCJQ-JJ-0879)+3 种基金by the National Key Research and Development Program of China(Grant No.2020YFA0709803)by the Science and Technology Innovation Program of Hunan Province(Grant Nos.2022RC1192,2021RC3082)by the Natural Science Foundation of Hunan(Grant No.2021JJ20053)by the National University of Defense Technology(Grant Nos.2023-lxy-fhjj-002,202401-YJRC-XX-001).
文摘In this paper,we develop the stabilization-free virtual element method for the Helmholtz transmission eigenvalue problem on anisotropic media.The eigenvalue problem is a variable-coefficient,non-elliptic,non-selfadjoint and nonlinear model.Separating the cases of the index of refraction n≠1 and n≡1,the stabilization-free virtual element schemes are proposed,respectively.Furthermore,we prove the spectral approximation property and error estimates in a unified theoretical framework.Finally,a series of numerical examples are provided to verify the theoretical results,show the benefits of the stabilization-free virtual element method applied to eigenvalue problems,and implement the extensions to high-order and high-dimensional cases.
