Cover Image

The $hp$-FEM applied to the Helmholtz equation with PML truncation does not suffer from the pollution effect

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Galkowski, Jeffrey, Lafontaine, David, Spence, Euan A., Wunsch, Jared
Format:	Preprint
Published:	2022
Subjects:	Analysis of PDEs Numerical Analysis
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Helmholtz boundary integral methods and the pollution effect
by: Galkowski, Jeffrey, et al.
Published: (2025)

Numerical analysis of the high-frequency Helmholtz equation using semiclassical analysis
by: Galkowski, Jeffrey, et al.
Published: (2025)

Convergence of overlapping domain decomposition methods with PML transmission conditions applied to nontrapping Helmholtz problems
by: Galkowski, Jeffrey, et al.
Published: (2024)

Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition
by: Lafontaine, David, et al.
Published: (2022)

Non-uniform finite-element meshes defined by ray dynamics for Helmholtz problems
by: Averseng, Martin, et al.
Published: (2025)

Sharp preasymptotic error bounds for the Helmholtz $h$-FEM
by: Galkowski, Jeffrey, et al.
Published: (2023)

Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies
by: Averseng, Martin, et al.
Published: (2023)

Convergence theory for two-level hybrid Schwarz preconditioners for high-frequency Helmholtz problems
by: Galkowski, Jeffrey, et al.
Published: (2025)

Schwarz methods with PMLs for Helmholtz problems: fast convergence at high frequency
by: Galkowski, Jeffrey, et al.
Published: (2024)

Preconditioning FEM discretisations of the high-frequency Helmholtz and Maxwell equations by either perturbing the coefficients or adding absorption
by: Spence, Euan A.
Published: (2025)

Helmholtz quasi-resonances are unstable under most single-signed perturbations of the wave speed
by: Spence, Euan A., et al.
Published: (2024)

The geometric error is less than the pollution error when solving the high-frequency Helmholtz equation with high-order FEM on curved domains
by: Chaumont-Frelet, Théophile, et al.
Published: (2024)

Wavenumber-explicit $hp$-FEM analysis of Maxwell's equations with impedance boundary conditions in piecewise smooth media
by: Melenk, Jens Markus, et al.
Published: (2026)

Coercive second-kind boundary integral equations for the Laplace Dirichlet problem on Lipschitz domains
by: Chandler-Wilde, Simon N., et al.
Published: (2022)

Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D
by: Faustmann, Markus, et al.
Published: (2022)

Sharp error bounds for edge-element discretisations of the high-frequency Maxwell equations
by: Chaumont-Frelet, Théophile, et al.
Published: (2024)

Propagation for Schrödinger operators with potentials singular along a hypersurface
by: Galkowski, Jeffrey, et al.
Published: (2023)

Wavenumber-explicit stability and convergence analysis of hp finite element discretizations of Helmholtz problems in piecewise smooth media
by: Bernkopf, M., et al.
Published: (2022)

Theory of two-level Schwarz preconditioners with piecewise-polynomial coarse spaces for the high-frequency Helmholtz equation
by: Graham, Ivan G., et al.
Published: (2025)

Fast convergent PML method for scattering with periodic surfaces: the exceptional case
by: Zhang, Ruming
Published: (2022)

p and hp Spectral Element Methods for Elliptic Boundary Layer Problems
by: Husain, Akhlaq, et al.
Published: (2024)

Two-level preconditioners for the Helmholtz equation
by: Bonazzoli, Marcella, et al.
Published: (2017)

The PML-Method for a Scattering Problem for a Local Perturbation of an Open Periodic Waveguide
by: Kirsch, Andreas, et al.
Published: (2024)

Massively parallel Schwarz methods for the high frequency Helmholtz equation
by: Xie, Yan, et al.
Published: (2026)

A mixed FEM for a time-fractional Fokker-Planck model
by: Karaa, Samir, et al.
Published: (2023)

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation
by: Faou, Erwan, et al.
Published: (2025)

Efficient approximation of high-frequency Helmholtz solutions by Gaussian coherent states
by: Chaumont-Frelet, T., et al.
Published: (2022)

An implementation of hp-FEM for the fractional Laplacian
by: Bahr, Björn, et al.
Published: (2024)

Analysis of a FEM-MCM Discretization for the 2D/3D stochastic closed-loop geothermal system
by: Qin, Yi, et al.
Published: (2023)

Lower bounds for piecewise polynomial approximations of oscillatory functions
by: Galkowski, Jeffrey
Published: (2022)

Duality analysis of interior penalty discontinuous Galerkin methods under minimal regularity and application to the a priori and a posteriori error analysis of Helmholtz problems
by: Chaumont-Frelet, T.
Published: (2022)

On a nonlinear nonlocal reaction-diffusion system applied to image restoration
by: Li, Yuhang, et al.
Published: (2024)

Numerical assessment of PML transmission conditions in a domain decomposition method for the Helmholtz equation
by: Bootland, Niall, et al.
Published: (2022)

Analysis and numerical analysis of the Helmholtz-Korteweg equation
by: Farrell, Patrick E., et al.
Published: (2025)

Wavenumber-explicit analytic regularity of the heterogeneous Maxwell equations with impedance boundary conditions
by: Melenk, Jens Markus, et al.
Published: (2026)

Nonlocal Stokes equation with relaxation on the divergence free equation
by: Zhang, Yajie, et al.
Published: (2024)

Quasi-optimal complexity $hp$-FEM for the Poisson Equation on a rectangle
by: Knook, Kars, et al.
Published: (2024)

Exponential Convergence of $hp$-FEM for the Integral Fractional Laplacian on cuboids
by: Bahr, Björn, et al.
Published: (2026)

To blow-up or not to blow-up for a granular kinetic equation
by: Carrillo, José A., et al.
Published: (2024)

Analysis of the $hp$-version of a first order system least squares method for the Helmholtz equation
by: Bernkopf, Maximilian, et al.
Published: (2018)