A pure source transfer domain decomposition method for Helmholtz equations in unbounded domain
From MaRDI portal
Publication:785551
DOI10.1007/s10915-020-01249-2OpenAlexW3035858788MaRDI QIDQ785551
Publication date: 7 August 2020
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1505.06052
Helmholtz equationpreconditionerdomain decomposition methodperfectly matched layerlarge wave numbersource transfer
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) PDEs in connection with optics and electromagnetic theory (35Q60) 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) Diffraction, scattering (78A45) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Preconditioners for iterative methods (65F08)
Related Items
Schwarz methods by domain truncation ⋮ Preasymptotic error analysis of the HDG method for Helmholtz equation with large wave number ⋮ Trace transfer-based diagonal sweeping domain decomposition method for the Helmholtz equation: algorithms and convergence analysis ⋮ Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation ⋮ Iterative Pure Source Transfer Domain Decomposition Methods for Helmholtz Equations in Heterogeneous Media ⋮ Double Source Transfer Domain Decomposition Method For Helmholtz Problems ⋮ A Diagonal Sweeping Domain Decomposition Method with Source Transfer for the Helmholtz Equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A rapidly converging domain decomposition method for the Helmholtz equation
- Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation
- Acoustic inverse scattering via Helmholtz operator factorization and optimization
- The method of polarized traces for the 2D Helmholtz equation
- Schwarz methods over the course of time
- Analysis of a Cartesian PML approximation to acoustic scattering problems in \(\mathbb R^2\)
- A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
- A perfectly matched layer for the absorption of electromagnetic waves
- Three-dimensional perfectly matched layer for the absorption of electromagnetic waves
- Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
- Analysis of a Cartesian PML approximation to acoustic scattering problems in \(\mathbb R^2\) and \(\mathbb R^3\)
- A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems
- Wideband nested cross approximation for Helmholtz problems
- An improved sweeping domain decomposition preconditioner for the Helmholtz equation
- A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
- A double-sweeping preconditioner for the Helmholtz equation
- Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis
- General DG-methods for highly indefinite Helmholtz problems
- Analysis of the PML equations in general convex geometry
- Additive Sweeping Preconditioner for the Helmholtz Equation
- Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: $hp$ Version
- A Source Transfer Domain Decomposition Method for Helmholtz Equations in Unbounded Domain
- Eliminating the pollution effect in Helmholtz problems by local subscale correction
- Using Plane Waves as Base Functions for Solving Time Harmonic Equations with the Ultra Weak Variational Formulation
- Convergence of the Uniaxial Perfectly Matched Layer Method for Time-Harmonic Scattering Problems in Two-Layered Media
- ℎ𝑝-Discontinuous Galerkin methods for the Helmholtz equation with large wave number
- Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
- Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
- Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The h-p Version of the FEM
- Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions
- Localization of elliptic multiscale problems
- Multilevel Preconditioner with Stable Coarse Grid Corrections for the Helmholtz Equation
- Wave-Number-Explicit Bounds in Time-Harmonic Scattering
- Optimized Multiplicative, Additive, and Restricted Additive Schwarz Preconditioning
- Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
- Plane wave discontinuous Galerkin methods: Analysis of theh-version
- A Fast Butterfly Algorithm for the Computation of Fourier Integral Operators
- An Adaptive Finite Element Method with Perfectly Matched Absorbing Layers for the Wave Scattering by Periodic Structures
- Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
- Directional ‐matrix compression for high‐frequency problems
- FEM and CIP-FEM for Helmholtz Equation with High Wave Number and Perfectly Matched Layer Truncation
- 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
- Optimized Schwarz Methods without Overlap for the Helmholtz Equation
- A new Heterogeneous Multiscale Method for the Helmholtz equation with high contrast
- Double Source Transfer Domain Decomposition Method For Helmholtz Problems
- An optimized Schwarz method with relaxation for the Helmholtz equation: the negative impact of overlap
- Preasymptotic Error Analysis of Higher Order FEM and CIP-FEM for Helmholtz Equation with High Wave Number
- An Additive Overlapping Domain Decomposition Method for the Helmholtz Equation
- The Mathematical Theory of Finite Element Methods
- Hierarchical matrix techniques for low- and high-frequency Helmholtz problems
- Pre-asymptotic error analysis of CIP-FEM and FEM for the Helmholtz equation with high wave number. Part I: linear version
