Multi-Resolution Localized Orthogonal Decomposition for Helmholtz Problems
From MaRDI portal
Publication:5099845
DOI10.1137/21M1414607zbMath1493.65204arXiv2104.11190OpenAlexW3153003118MaRDI QIDQ5099845
Moritz Hauck, Daniel Peterseim
Publication date: 26 August 2022
Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2104.11190
wave propagationheterogeneous mediamulti-level methodnumerical homogenizationHelmholtz problemmulti-resolution decomposition
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)
Related Items (8)
Neural Network Approximation of Coarse-Scale Surrogates in Numerical Homogenization ⋮ A multiscale method for inhomogeneous elastic problems with high contrast coefficients ⋮ Wavenumber Explicit Convergence of a Multiscale Generalized Finite Element Method for Heterogeneous Helmholtz Problems ⋮ Does the Helmholtz Boundary Element Method Suffer from the Pollution Effect? ⋮ Numerical multiscale methods for waves in high-contrast media ⋮ An Improved High-Order Method for Elliptic Multiscale Problems ⋮ Exponentially Convergent Multiscale Methods for 2D High Frequency Heterogeneous Helmholtz Equations ⋮ Super-localization of elliptic multiscale problems
Cites Work
- Unnamed Item
- Unnamed Item
- Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed?
- Mathematical aspects of discontinuous Galerkin methods.
- Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients
- The many proofs of an identity on the norm of oblique projections
- The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances
- Efficient implementation of the localized orthogonal decomposition method
- Stability estimate for the Helmholtz equation with rapidly jumping coefficients
- Wavenumber-explicit convergence analysis for finite element discretizations of time-harmonic wave propagation problems with perfectly matched layers
- Stability estimates for a class of Helmholtz problems
- Stable multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering
- On Stability of Discretizations of the Helmholtz Equation
- Multigrid with Rough Coefficients and Multiresolution Operator Decomposition from Hierarchical Information Games
- Variational Multiscale Stabilization and the Exponential Decay of Fine-Scale Correctors
- Eliminating the pollution effect in Helmholtz problems by local subscale correction
- Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation
- Localization of elliptic multiscale problems
- A Class of Bases in $L^2$ for the Sparse Representation of Integral Operators
- An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
- An analysis of the convergence of mixed finite element methods
- Numerical Methods for Elliptic and Parabolic Partial Differential Equations
- Multiscale Petrov-Galerkin Method for High-Frequency Heterogeneous Helmholtz Equations
- Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in two dimensions
- Numerical Homogenization of H(curl)-Problems
- A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods
- Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
- A High-Order Approach to Elliptic Multiscale Problems with General Unstructured Coefficients
- Multiscale scattering in nonlinear Kerr-type media
- Computational high frequency scattering from high-contrast heterogeneous media
- Sparse Compression of Expected Solution Operators
- Numerical Homogenization by Localized Orthogonal Decomposition
- Stability and finite element error analysis for the Helmholtz equation with variable coefficients
- Finite element quasi-interpolation and best approximation
- Oversampling for the Multiscale Finite Element Method
- The Mathematical Theory of Finite Element Methods
- Numerical homogenization beyond scale separation
This page was built for publication: Multi-Resolution Localized Orthogonal Decomposition for Helmholtz Problems
