Dirac assisted tree method for 1D heterogeneous Helmholtz equations with arbitrary variable wave numbers

DOI10.1016/J.CAMWA.2021.06.015OpenAlexW3094825971WikidataQ112880457 ScholiaQ112880457MaRDI QIDQ2047600

Yanyan Li

Publication date: 20 August 2021

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.01295

zbMATH Keywords

compact finite difference methodnumerical dispersionaccuracy orderDirac assisted tree (DAT) methodheterogeneous Helmholtz equationvariable wave number

Mathematics Subject Classification ID

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

Related Items (5)

A high order compact finite difference scheme for elliptic interface problems with discontinuous and high-contrast coefficients ⋮ Sharp Wavenumber-Explicit Stability Bounds for 2D Helmholtz Equations ⋮ Sixth-Order Compact Finite Difference Method for 2D Helmholtz Equations with Singular Sources and Reduced Pollution Effect ⋮ Asymptotic Dispersion Correction in General Finite Difference Schemes for Helmholtz Problems ⋮ Sixth order compact finite difference schemes for Poisson interface problems with singular sources

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analysis of a fast method for solving the high frequency Helmholtz equation in one dimension
• The partition of unity finite element method: basic theory and applications
• Framelets and wavelets. Algorithms, analysis, and applications
• The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances
• An optimal compact sixth-order finite difference scheme for the Helmholtz equation
• Solving Helmholtz equation at high wave numbers in exterior domains
• Wave interpolation finite elements for Helmholtz problems with jumps in the wave speed
• High-order finite difference methods for the Helmholtz equation
• On high order methods for the heterogeneous Helmholtz equation
• Dispersion correction for Helmholtz in 1D with piecewise constant wavenumber
• 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
• Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number
• Linear continuous interior penalty finite element method for Helmholtz equation With High Wave Number: One-Dimensional Analysis
• Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: $hp$ Version
• On the Derivation of Highest-Order Compact Finite Difference Schemes for the One- and Two-Dimensional Poisson Equation with Dirichlet Boundary Conditions
• High Order Compact Finite Difference Schemes for the Helmholtz Equation with Discontinuous Coefficients
• Overview of the discontinuous enrichment method, the ultra-weak variational formulation, and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons
• Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
• A Survey of Trefftz Methods for the Helmholtz Equation
• Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
• Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
• THE PARTITION OF UNITY METHOD
• 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
• A high-order compact scheme for the one-dimensional Helmholtz equation with a discontinuous coefficient
• DEVELOPMENT OF A THREE-POINT SIXTH-ORDER HELMHOLTZ SCHEME
• A Finite Difference Method with Optimized Dispersion Correction for the Helmholtz Equation
• Is Pollution Effect of Finite Difference Schemes Avoidable for Multi-Dimensional Helmholtz Equations with High Wave Numbers?
• Stability and finite element error analysis for the Helmholtz equation with variable coefficients
• Fourth-Order Compact Schemes for Helmholtz Equations with Piecewise Wave Numbers in the Polar Coordinates
• Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes
• Multigrid methods for Helmholtz problems: A convergent scheme in 1D using standard components
• A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
• Acoustic and electromagnetic equations. Integral representations for harmonic problems

This page was built for publication: Dirac assisted tree method for 1D heterogeneous Helmholtz equations with arbitrary variable wave numbers