Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification
DOI10.1007/s10444-021-09889-0zbMath1473.35122arXiv2005.13390OpenAlexW3184294135MaRDI QIDQ2230585
O. R. Pembery, Ivan G. Graham, Euan A. Spence
Publication date: 24 September 2021
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.13390
Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08)
Related Items (1)
Uses Software
Cites Work
- A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
- Some observations on weighted GMRES
- Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed?
- Finite element analysis of acoustic scattering
- Weighted FOM and GMRES for solving nonsymmetric linear systems
- Distribution of resonances and local energy decay in the transmission problem. II
- The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances
- Wavenumber-explicit analysis for the Helmholtz \(h\)-BEM: error estimates and iteration counts for the Dirichlet problem
- Iterative solution of systems of linear equations arising in the context of stochastic finite elements
- On a class of preconditioners for solving the Helmholtz equation
- Stability estimate for the Helmholtz equation with rapidly jumping coefficients
- A coercive heterogeneous media Helmholtz model: formulation, wavenumber-explicit analysis, and preconditioned high-order FEM
- Optimal constants in nontrapping resolvent estimates and applications in numerical analysis
- Fourier integral operators. II
- Numerical solution of spectral stochastic finite element systems
- Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: $hp$ Version
- Wavenumber-Explicit Bounds in Time-Harmonic Acoustic Scattering
- Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption
- Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
- Firedrake
- Singularities of boundary value problems. II
- Wave-Number-Explicit Bounds in Time-Harmonic Scattering
- Efficient Solvers for a Linear Stochastic Galerkin Mixed Formulation of Diffusion Problems with Random Data
- Block-diagonal preconditioning for spectral stochastic finite-element systems
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- Boundary Conditions for the Numerical Solution of Elliptic Equations in Exterior Regions
- Domain Decomposition Algorithms for Indefinite Elliptic Problems
- Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
- ON THE SHORT WAVE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF STATIONARY PROBLEMS AND THE ASYMPTOTIC BEHAVIOUR ASt→ ∞ OF SOLUTIONS OF NON-STATIONARY PROBLEMS
- On George’s Nested Dissection Method
- Singularities of boundary value problems. I
- A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods
- Acoustic transmission problems: Wavenumber-explicit bounds and resonance-free regions
- An Improved Spectral Graph Partitioning Algorithm for Mapping Parallel Computations
- Efficient Spectral Stochastic Finite Element Methods for Helmholtz Equations with Random Inputs
- Domain decomposition preconditioners for high-order discretizations of the heterogeneous Helmholtz equation
- Wavenumber explicit convergence analysis for finite element discretizations of general wave propagation problems
- Domain Decomposition with Local Impedance Conditions for the Helmholtz Equation with Absorption
- Quasi-Monte Carlo Finite Element Analysis for Wave Propagation in Heterogeneous Random Media
- Is the Helmholtz Equation Really Sign-Indefinite?
- Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption
- Stability and finite element error analysis for the Helmholtz equation with variable coefficients
- Preasymptotic Error Analysis of Higher Order FEM and CIP-FEM for Helmholtz Equation with High Wave Number
- The Mathematical Theory of Finite Element Methods
- Some Remarks on the Elman Estimate for GMRES
- Pre-asymptotic error analysis of CIP-FEM and FEM for the Helmholtz equation with high wave number. Part I: linear version
- Boundary Element Methods
- Acoustic and electromagnetic equations. Integral representations for harmonic problems
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification