A new multigrid finite element method for the transmission eigenvalue problems

DOI10.1016/j.amc.2016.07.022zbMath1410.65448arXiv1601.02361OpenAlexW2234487617MaRDI QIDQ1732822

Hai Bi, Yidu Yang, JiaYu Han

Publication date: 25 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.02361

zbMATH Keywords

multigrid methodtransmission eigenvaluesnonsymmetric eigenvalue problems

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items

Convergence of a lowest-order finite element method for the transmission eigenvalue problem ⋮ Newton-type multilevel optimization method ⋮ Virtual element method for the Helmholtz transmission eigenvalue problem of anisotropic media ⋮ On trajectories of complex-valued interior transmission eigenvalues ⋮ Discontinuous Galerkin method for the interior transmission eigenvalue problem in inverse scattering theory ⋮ Nonconforming virtual element discretization for the transmission eigenvalue problem ⋮ A virtual element method for the transmission eigenvalue problem ⋮ A two-grid discretization scheme of non-conforming finite elements for transmission eigenvalues ⋮ The method of fundamental solutions for computing acoustic interior transmission eigenvalues ⋮ A \(C^1-C^0\) conforming virtual element discretization for the transmission eigenvalue problem ⋮ Ground-state solutions to a Kirchhoff-type transmission problem ⋮ Ground-state solutions to Kirchhoff-type transmission problems with critical perturbation ⋮ A cascadic multigrid method for nonsymmetric eigenvalue problem ⋮ A lowest-order virtual element method for the Helmholtz transmission eigenvalue problem ⋮ Virtual Elements for the Transmission Eigenvalue Problem on Polytopal Meshes ⋮ Order Reduced Schemes for the Fourth Order Eigenvalue Problems on Multi-Connected Planar Domains ⋮ A multigrid correction scheme for a new Steklov eigenvalue problem in inverse scattering

Uses Software

• iFEM

Cites Work

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• A multigrid method for Helmholtz transmission eigenvalue problems
• Error analysis for the finite element approximation of transmission eigenvalues
• A multigrid method for eigenvalue problem
• The interior transmission problem
• Inverse acoustic and electromagnetic scattering theory.
• A multilevel correction method for convection-diffusion eigenvalue problems
• A multilevel correction method for interior transmission eigenvalue problem
• The multilevel mixed finite element discretizations based on local defect-correction for the Stokes eigenvalue problem
• Local and parallel finite element algorithms for eigenvalue problems
• On the existence of transmission eigenvalues
• A spectral-element method for transmission eigenvalue problems
• A two-level method for nonsymmetric eigenvalue problems
• The Existence of an Infinite Discrete Set of Transmission Eigenvalues
• Iterative Methods for Transmission Eigenvalues
• The Interior Transmission Problem and Inverse Scattering from Inhomogeneous Media
• The Shifted-Inverse Iteration Based on the Multigrid Discretizations for Eigenvalue Problems
• Transmission eigenvalues and the nondestructive testing of dielectrics
• Analytical and computational methods for transmission eigenvalues
• The inverse electromagnetic scattering problem for anisotropic media
• Three-Scale Finite Element Discretizations for Quantum Eigenvalue Problems
• Transmission Eigenvalues
• On the boundary value problem of the biharmonic operator on domains with angular corners
• A two-grid discretization scheme for eigenvalue problems
• On the existence of transmission eigenvalues in an inhomogeneous medium
• A multi-level correction scheme for eigenvalue problems