Complete radiation boundary conditions for the Helmholtz equation. II: Domains with corners
DOI10.1007/s00211-023-01352-0zbMath1519.65054OpenAlexW4366758567MaRDI QIDQ6044434
Thomas M. Hagstrom, Seungil Kim
Publication date: 19 May 2023
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00211-023-01352-0
absorbing boundary conditionscatteringeigenvalue problemHelmholtz equationwaveguidesradiation boundary condition
Asymptotic behavior of solutions to PDEs (35B40) Wave scattering in solid mechanics (74J20) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Diffraction, scattering (78A45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Antennas, waveguides in optics and electromagnetic theory (78A50) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Waves and radiation in optics and electromagnetic theory (78A40) Elliptic functions and integrals (33E05) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Error analysis of the DtN-FEM for the scattering problem in acoustics via Fourier analysis
- Complete radiation boundary conditions for the Helmholtz equation. I: Waveguides
- A perfectly matched layer for the Helmholtz equation in a semi-infinite strip
- Pole condition: A numerical method for Helmholtz-type scattering problems with inhomogeneous exterior domain
- Analysis of a Cartesian PML approximation to acoustic scattering problems in \(\mathbb R^2\)
- The PML for rough surface scattering
- Exact non-reflecting boundary conditions
- Bayliss-Turkel-like radiation conditions on surfaces of arbitrary shape
- On nonreflecting boundary conditions
- Hybrid absorbing boundary conditions of PML and CRBC
- Corner treatments for high-order local absorbing boundary conditions in high-frequency acoustic scattering
- Application of a complete radiation boundary condition for the Helmholtz equation in locally perturbed waveguides
- An improved surface radiation condition for high-frequency acoustic scattering problems
- A new auxiliary variable formulation of high-order local radiation boundary conditions: corner compatibility conditions and extensions to first-order systems
- Near-Optimal Perfectly Matched Layers for Indefinite Helmholtz Problems
- Convergence of the Uniaxial Perfectly Matched Layer Method for Time-Harmonic Scattering Problems in Two-Layered Media
- Complete Radiation Boundary Conditions: Minimizing the Long Time Error Growth of Local Methods
- Comparison of high-order absorbing boundary conditions and perfectly matched layers in the frequency domain
- Electromagnetic Scattering by Unbounded Rough Surfaces
- Second-Order Absorbing Boundary Conditions for the Wave Equation: A Solution for the Corner Problem
- Numerical accuracy of a Padé-type non-reflecting boundary condition for the finite element solution of acoustic scattering problems at high-frequency
- Analysis of a finite PML approximation for the three dimensional time-harmonic Maxwell and acoustic scattering problems
- Continued fraction absorbing boundary conditions for convex polygonal domains
- deal.II—A general-purpose object-oriented finite element library
- Higher Order Paraxial Wave Equation Approximations in Heterogeneous Media
- Boundary Conditions for the Numerical Solution of Elliptic Equations in Exterior Regions
- Absorbing Boundary Conditions for the Numerical Simulation of Waves
- Absorbing boundary conditions for numerical simulation of waves
- Solving Time-Harmonic Scattering Problems Based on the Pole Condition I: Theory
- Solving Time-Harmonic Scattering Problems Based on the Pole Condition II: Convergence of the PML Method
- A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach
- Mathematical analysis of absorbing boundary conditions for the wave equation: the corner problem
- Finite Elements for Helmholtz Equations with a Nonlocal Boundary Condition
- Variational Approach in Weighted Sobolev Spaces to Scattering by Unbounded Rough Surfaces
- Error analysis of PML-FEM approximations for the Helmholtz equation in waveguides
- An Adaptive Perfectly Matched Layer Technique for Time-harmonic Scattering Problems
