Sixth-Order Compact Finite Difference Method for 2D Helmholtz Equations with Singular Sources and Reduced Pollution Effect

DOI10.4208/cicp.oa-2023-0062arXiv2112.07154OpenAlexW4387393792MaRDI QIDQ6142995

No author found.

Publication date: 4 January 2024

Published in: Communications in Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.07154

zbMATH Keywords

interfacemixed boundary conditionsHelmholtz equationfinite differencepollution effectcorner treatmentpollution minimization

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (1)

Sixth-order hybrid finite difference methods for elliptic interface problems with mixed boundary conditions

Cites Work

• Unnamed Item
• Unnamed Item
• A compact fourth order scheme for the Helmholtz equation in polar coordinates
• An optimal 25-point finite difference scheme for the Helmholtz equation with PML
• High order matched interface and boundary methods for the Helmholtz equation in media with arbitrarily curved interfaces
• An optimal compact sixth-order finite difference scheme for the Helmholtz equation
• The method of difference potentials for the Helmholtz equation using compact high order schemes
• Pollution and accuracy of solutions of the Helmholtz equation: a novel perspective from the eigenvalues
• Dirac assisted tree method for 1D heterogeneous Helmholtz equations with arbitrary variable wave numbers
• A high order compact FD framework for elliptic BVPs involving singular sources, interfaces, and irregular domains
• A high order compact finite difference scheme for elliptic interface problems with discontinuous and high-contrast coefficients
• A fourth-order optimal finite difference scheme for the Helmholtz equation with PML
• Sixth-order finite difference scheme for the Helmholtz equation with inhomogeneous Robin boundary condition
• An optimal 13-point finite difference scheme for a 2D Helmholtz equation with a perfectly matched layer boundary condition
• Sixth order compact finite difference schemes for Poisson interface problems with singular sources
• Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number
• Stability estimates for a class of Helmholtz problems
• A High-Order Numerical Method for the Helmholtz Equation with Nonstandard Boundary Conditions
• High Order Compact Finite Difference Schemes for the Helmholtz Equation with Discontinuous Coefficients
• Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
• A Survey of Trefftz Methods for the Helmholtz Equation
• Eliminating the pollution effect in Helmholtz problems by local subscale correction
• Computational Ocean Acoustics
• ℎ𝑝-Discontinuous Galerkin methods for the Helmholtz equation with large wave number
• Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
• Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The h-p Version of the FEM
• Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
• Matched interface and boundary (MIB) for the implementation of boundary conditions in high-order central finite differences
• Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
• A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods
• Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number
• Wavelet-based Edge Multiscale Finite Element Method for Helmholtz problems in perforated domains
• Sharp Wavenumber-Explicit Stability Bounds for 2D Helmholtz Equations
• Is Pollution Effect of Finite Difference Schemes Avoidable for Multi-Dimensional Helmholtz Equations with High Wave Numbers?
• A Multigrid Method for the Helmholtz Equation with Optimized Coarse Grid Corrections
• Stability and finite element error analysis for the Helmholtz equation with variable coefficients
• Preasymptotic Error Analysis of Higher Order FEM and CIP-FEM for Helmholtz Equation with High Wave Number
• Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes
• A Fast Algorithm for the Electromagnetic Scattering from a Large Cavity
• A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
• Closed Form Dispersion Corrections Including a Real Shifted WaveNumber for Finite Difference Discretizations of 2D Constant Coefficient Helmholtz Problems
• High Order Compact Schemes for Flux Type BCs
• Acoustic and electromagnetic equations. Integral representations for harmonic problems

This page was built for publication: Sixth-Order Compact Finite Difference Method for 2D Helmholtz Equations with Singular Sources and Reduced Pollution Effect