Iterative solution of Helmholtz problem with high-order isogeometric analysis and finite element method at mid-range frequencies
From MaRDI portal
Publication:2309347
DOI10.1016/j.cma.2020.112855zbMath1436.78007OpenAlexW2998949721MaRDI QIDQ2309347
Ganesh C. Diwan, M. Shadi Mohamed
Publication date: 31 March 2020
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2020.112855
finite element methodpreconditioningHelmholtz equationiterative solverisogeometric analysisshifted-Laplace preconditioner
Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)
Related Items (5)
Automatic stabilization of finite-element simulations using neural networks and hierarchical matrices ⋮ Novel adaptive finite volume method on unstructured meshes for time-domain wave scattering and diffraction ⋮ Isogeometric Solution of Helmholtz Equation with Dirichlet Boundary Condition in Regions with Irregular Boundary: Numerical Experiences ⋮ Iterative solution with shifted Laplace preconditioner for plane wave enriched isogeometric analysis and finite element discretization for high-frequency acoustics ⋮ Towards accuracy and scalability: combining isogeometric analysis with deflation to obtain scalable convergence for the Helmholtz equation
Uses Software
Cites Work
- 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?
- A fast method for the solution of the Helmholtz equation
- An iterative method for the Helmholtz equation
- Preconditioning techniques for the solution of the Helmholtz equation by the finite element method
- Isogeometric analysis in electromagnetics: B-splines approximation
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- Advances in iterative methods and preconditioners for the Helmholtz equation
- On a multilevel Krylov method for the Helmholtz equation preconditioned by shifted Laplacian
- Preconditioning Helmholtz linear systems
- The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations
- Wave-ray multigrid method for standing wave equations
- Can coercive formulations lead to fast and accurate solution of the Helmholtz equation?
- Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation
- Computational aspects of the ultra-weak variational formulation
- Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
- Pollution studies for high order isogeometric analysis and finite element for acoustic problems
- Optimal reduction of numerical dispersion for wave propagation problems. I: Application to 1-d isogeometric elements
- Plane wave enriched partition of unity isogeometric analysis (PUIGA) for 2D-Helmholtz problems
- A performance study of NURBS-based isogeometric analysis for interior two-dimensional time-harmonic acoustics
- A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
- Iterative schemes for high order compact discretizations to the exterior Helmholtz equation
- A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations
- Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
- 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
- A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
- Isogeometric Analysis
- ILUT: A dual threshold incomplete LU factorization
- Schwarz Domain Decomposition Preconditioners for Plane Wave Discontinuous Galerkin Methods
- The Multilevel Krylov-Multigrid Method for the Helmholtz Equation Preconditioned by the Shifted Laplacian
- Algorithm 832
- A scalable multigrid method for solving indefinite Helmholtz equations with constant wave numbers
- How Large a Shift is Needed in the Shifted Helmholtz Preconditioner for its Effective Inversion by Multigrid?
This page was built for publication: Iterative solution of Helmholtz problem with high-order isogeometric analysis and finite element method at mid-range frequencies
