Quasi-local and frequency-robust preconditioners for the Helmholtz first-kind integral equations on the disk
DOI10.1051/m2an/2023105zbMATH Open1541.65171MaRDI QIDQ6552259
Martin Averseng, François Alouges
Publication date: 8 June 2024
Published in: European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Numerical methods for integral equations (65R20) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38) Integral representations, integral operators, integral equations methods in two dimensions (31A10) Singularity in context of PDEs (35A21) Preconditioners for iterative methods (65F08) Integro-partial differential equations (35R09) Green's functions for elliptic equations (35J08)
Cites Work
- Unnamed Item
- Unnamed Item
- Approximating gradients with continuous piecewise polynomial functions
- Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed?
- A stable well-conditioned integral equation for electromagnetism scattering
- Boundary integral equations for screen problems in \({\mathbb{R}}^ 3\)
- The construction of some efficient preconditioners in the boundary element method
- A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
- Diagonal forms of translation operators for the Helmholtz equation in three dimensions
- The \(h\)-\(p\) boundary element method for solving 2- and 3-dimensional problems
- Wavenumber-explicit analysis for the Helmholtz \(h\)-BEM: error estimates and iteration counts for the Dirichlet problem
- Closed-form inverses of the weakly singular and hypersingular operators on disks
- The \(hp\)-version of the boundary element method for Helmholtz screen problems
- Optimal operator preconditioning for pseudodifferential boundary problems
- New preconditioners for the Laplace and Helmholtz integral equations on open curves: analytical framework and numerical results
- Operator preconditioning
- The weighted Poincaré inequalities.
- Some Extensions of W. Gautschi's Inequalities for the Gamma Function
- Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation
- Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- An Optimal Order Process for Solving Finite Element Equations
- How Fast are Nonsymmetric Matrix Iterations?
- A Padé Approximation Method for Square Roots of Symmetric Positive Definite Matrices
- Des préconditionneurs pour la résolution numérique des équations intégrales de frontière de l'acoustique
- Asymptotics Without Logarithmic Terms for Crack Problems†
- Weighted Poincare inequalities
- FEM and BEM simulations with the Gypsilab framework
- About Some Boundary Integral Operators on the Unit Disk Related to the Laplace Equation
- Mesh-Independent Operator Preconditioning for Boundary Elements on Open Curves
- Computational Software: Simple FMM Libraries for Electrostatics, Slow Viscous Flow, and Frequency-Domain Wave Propagation
- Anisotropic Mesh Refinement: The Conditioning of Galerkin Boundary Element Matrices and Simple Preconditioners
- Boundary Element Methods
- A fast algorithm for particle simulations
- Acoustic and electromagnetic equations. Integral representations for harmonic problems
- Stability of a weighted \(L^2\) projection in a weighted Sobolev norm
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