The Helmholtz equation with uncertainties in the wavenumber
DOI10.1007/s10915-024-02450-3arXiv2209.14740OpenAlexW4391538223MaRDI QIDQ6191362
Publication date: 9 February 2024
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2209.14740
GMRESHelmholtz equationpolynomial chaosstochastic Galerkin methodcomplex shifted Laplace preconditionermean value preconditioner
Probabilistic models, generic numerical methods in probability and statistics (65C20) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) PDEs with randomness, stochastic partial differential equations (35R60) Finite difference methods for boundary value problems involving PDEs (65N06) Preconditioners for iterative methods (65F08)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- 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?
- On the indefinite Helmholtz equation: Complex stretched absorbing boundary layers, iterative analysis, and preconditioning
- Accelerating the shifted Laplace preconditioner for the Helmholtz equation by multilevel deflation
- Modern solvers for Helmholtz problems
- Advances in iterative methods and preconditioners for the Helmholtz equation
- Efficient stochastic Galerkin methods for random diffusion equations
- Polynomial chaos for simulating random volatilities
- Finite element analysis of acoustic scattering
- On a class of preconditioners for solving the Helmholtz equation
- Stability-preserving model order reduction for linear stochastic Galerkin systems
- Poly-Sinc solution of stochastic elliptic differential equations
- Preconditioning the Helmholtz equation with the shifted Laplacian and Faber polynomials
- Generalised polynomial chaos for a class of linear conservation laws
- Numerical treatment of partial differential equations. Revised translation of the 3rd German edition of `Numerische Behandlung partieller Differentialgleichungen' by Martin Stynes.
- An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation
- Numerical solution of spectral stochastic finite element systems
- An adaptive stochastic Galerkin method for random elliptic operators
- Local Fourier analysis of the complex shifted Laplacian preconditioner for Helmholtz problems
- Essential Partial Differential Equations
- Use of Shifted Laplacian Operators for Solving Indefinite Helmholtz Equations
- Spectral Analysis of the Discrete Helmholtz Operator Preconditioned with a Shifted Laplacian
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- On the Spectrum of Deflated Matrices with Applications to the Deflated Shifted Laplace Preconditioner for the Helmholtz Equation
- LOCALIZED STOCHASTIC GALERKIN METHODS FOR HELMHOLTZ PROBLEMS CLOSE TO RESONANCE
- Inverse acoustic and electromagnetic scattering theory
This page was built for publication: The Helmholtz equation with uncertainties in the wavenumber
