A rapidly converging domain decomposition method for the Helmholtz equation
arXiv:1208.3956 · doi:10.1016/j.jcp.2013.01.039
Abstract
A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D Helmholtz equations. Transmission conditions based on the perfectly matched layer (PML) are derived that avoid artificial reflections and match incoming and outgoing waves at the subdomain interfaces. We focus on a subdivision of the rectangular domain into many thin subdomains along one of the axes, in combination with a certain ordering for solving the subdomain problems and a GMRES outer iteration. When combined with multifrontal methods, the solver has near-linear cost in examples, due to very small iteration numbers that are essentially independent of problem size and number of subdomains. It is to our knowledge only the second method with this property next to the moving PML sweeping method.
16 pages, 3 figures, 6 tables - v2 accepted for publication in the Journal of Computational Physics
References in corpus (1)
Cited by in corpus (39)
- A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media
- Overlapping domains for topology optimization of large-area metasurfaces
- A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations
- A multigrid method for the Helmholtz equation with optimized coarse grid corrections
- A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory
- L-Sweeps: A scalable, parallel preconditioner for the high-frequency Helmholtz equation
- An improved sweeping domain decomposition preconditioner for the Helmholtz equation
- Schwarz methods by domain truncation
- An Additive Overlapping Domain Decomposition Method for the Helmholtz Equation
- Recursive Sweeping Preconditioner for the 3D Helmholtz Equation
- Multidirectionnal sweeping preconditioners with non-overlapping checkerboard domain decomposition for Helmholtz problems
- A hybrid approach to solve the high-frequency Helmholtz equation with source singularity in smooth heterogeneous media
- Multitrace formulations and Domain Decomposition Methods for the solution of Helmholtz transmission problems for bounded composite scatterers
- Natural domain decomposition algorithms for the solution of time-harmonic elastic waves
- Domain Decomposition with local impedance conditions for the Helmholtz equation with absorption
- A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods
- Domain Decomposition Methods based on quasi-optimal transmission operators for the solution of Helmholtz transmission problems
- A hybrid shifted Laplacian multigrid and domain decomposition preconditioner for the elastic Helmholtz equations
- An Overlapping Domain Decomposition Preconditioner for the Helmholtz equation
- Sparsify and sweep: an efficient preconditioner for the Lippmann-Schwinger equation
- A Unified Framework for Double Sweep Methods for the Helmholtz Equation
- Solving the 3D High-Frequency Helmholtz Equation using Contour Integration and Polynomial Preconditioning
- A matrix-free parallel solution method for the three-dimensional heterogeneous Helmholtz equation
- A Fast Propagation Method for the Helmholtz equation
- A domain decomposition preconditioning for the integral equation formulation of the inverse scattering problem
- Additive Sweeping Preconditioner for the Helmholtz Equation
- Compressed absorbing boundary conditions via matrix probing
- A matrix-free parallel two-level deflation preconditioner for the two-dimensional Helmholtz problems
- A short note on the nested-sweep polarized traces method for the 2D Helmholtz equation
- Adaptive BDDC algorithms for the system arising from plane wave discretization of Helmholtz equations
- A two-grid method with dispersion matching for finite-element Helmholtz problems
- Numerical analysis of the high-frequency Helmholtz equation using semiclassical analysis
- Application of adapted-bubbles to the Helmholtz equation with large wave numbers in 2d
- Trace Transfer-based Diagonal Sweeping Domain Decomposition Method for the Helmholtz Equation: Algorithms and Convergence Analysis
- A diagonal sweeping domain decomposition method with source transfer for the Helmholtz equation
- Non-iterative domain decomposition for the Helmholtz equation using the method of difference potentials
- Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator
- The method of polarized traces for the 2D Helmholtz equation
- Compressed Absorbing Boundary Conditions for the Helmholtz Equation