Analysis of Schwarz Methods for Convected Helmholtz-Like Equations

DOI10.1137/23m1560057OpenAlexW4390697234MaRDI QIDQ6177442

Martin J. Gander, Antoine Tonnoir

Publication date: 17 January 2024

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/23m1560057

zbMATH Keywords

Schwarz methodsconvected Helmholtz equationcomplex advection

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Iterative numerical methods for linear systems (65F10) NLS equations (nonlinear Schrödinger equations) (35Q55) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Preconditioners for iterative methods (65F08) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

• Unnamed Item
• Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
• On the influence of geometry on optimized Schwarz methods
• Wave-ray multigrid method for standing wave equations
• Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems
• A domain decomposition preconditioner for an advection-diffusion problem
• Dirichlet-to-Neumann operator for diffraction problems in stratified anisotropic acoustic waveguides
• A non-overlapping domain decomposition method for the advection-diffusion problem
• Analysis of the SORAS domain decomposition preconditioner for non-self-adjoint or indefinite problems
• Stable perfectly matched layers with Lorentz transformation for the convected Helmholtz equation
• Low-order Prandtl-Glauert-Lorentz based absorbing boundary conditions for solving the convected Helmholtz equation with discontinuous Galerkin methods
• Corner treatments for high-order local absorbing boundary conditions in high-frequency acoustic scattering
• A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics
• Discrete optimization of Robin transmission conditions for anisotropic diffusion with discrete duality finite volume methods
• Optimized Schwarz methods for a diffusion problem with discontinuous coefficient
• Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation
• Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
• Perfectly matched transmission problem with absorbing layers: Application to anisotropic acoustics in convex polygonal domains
• Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption
• Optimized Schwarz Methods for the Time-Harmonic Maxwell Equations with Damping
• An algebraic multigrid wave–ray algorithm to solve eigenvalue problems for the helmholtz operator
• An Introduction to Domain Decomposition Methods
• An optimized Schwarz method with two-sided Robin transmission conditions for the Helmholtz equation
• Domain Decomposition Algorithms for Indefinite Elliptic Problems
• Computation of Ground States of the Gross--Pitaevskii Functional via Riemannian Optimization
• A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods
• Perfectly Matched Layers for the Convected Helmholtz Equation
• Optimized Schwarz Methods without Overlap for the Helmholtz Equation
• Construction and Numerical Assessment of Local Absorbing Boundary Conditions for Heterogeneous Time-Harmonic Acoustic Problems
• Domain Decomposition with Local Impedance Conditions for the Helmholtz Equation with Absorption
• Optimized Schwarz methods for unsymmetric layered problems with strongly discontinuous and anisotropic coefficients
• Accuracy Properties of the Wave‐Ray Multigrid Algorithm for Helmholtz Equations
• Schwarz methods by domain truncation
• Optimized Schwarz Methods with Overlap for the Helmholtz Equation
• Travelling waves for the nonlinear Schrödinger equation with general nonlinearity in dimension two
• Closed Form Optimized Transmission Conditions for Complex Diffusion with Many Subdomains
• Construction and analysis of a HDG solution for the total-flux formulation of the convected Helmholtz equation
• NonLocal Optimized Schwarz Method for the Helmholtz Equation with Physical Boundaries