Iterative solvers for coupled fluid-solid scattering
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Efficient harmonic balance simulation using multi-level frequency decomposition
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Multigrid Methods: Managing Massive Meshes
Computing in Science and Engineering
A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation
Journal of Computational Physics
Controllability method for the Helmholtz equation with higher-order discretizations
Journal of Computational Physics
Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation
Computers & Mathematics with Applications
Journal of Computational Physics
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
A domain decomposition solver for acoustic scattering by elastic objects in layered media
Journal of Computational Physics
A damping preconditioner for time-harmonic wave equations in fluid and elastic material
Journal of Computational Physics
Iterative solvers for coupled fluid--solid scattering
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Preconditioning Helmholtz linear systems
Applied Numerical Mathematics
Journal of Computational Physics
Acoustic inverse scattering via Helmholtz operator factorization and optimization
Journal of Computational Physics
A fast method for the solution of the Helmholtz equation
Journal of Computational Physics
A composite preconditioner for the electromagnetic scattering from a large cavity
Journal of Computational Physics
GPU implementation of a Helmholtz Krylov solver preconditioned by a shifted Laplace multigrid method
Journal of Computational and Applied Mathematics
Compact Fourier Analysis for Multigrid Methods based on Block Symbols
SIAM Journal on Matrix Analysis and Applications
Robust and highly scalable parallel solution of the Helmholtz equation with large wave numbers
Journal of Computational and Applied Mathematics
Three-dimensional visco-acoustic modeling using a renormalized integral equation iterative solver
Journal of Computational Physics
Newton multigrid least-squares FEM for the V-V-P formulation of the Navier-Stokes equations
Journal of Computational Physics
A robust multilevel method for hybridizable discontinuous Galerkin method for the Helmholtz equation
Journal of Computational Physics
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Standard multigrid algorithms have proven ineffective for the solution of discretizations of Helmholtz equations. In this work we modify the standard algorithm by adding GMRES iterations at coarse levels and as an outer iteration. We demonstrate the algorithm's effectiveness through theoretical analysis of a model problem and experimental results. In particular, we show that the combined use of GMRES as a smoother and outer iteration produces an algorithm whose performance depends relatively mildly on wave number and is robust for normalized wave numbers as large as 200. For fixed wave numbers, it displays grid-independent convergence rates and has costs proportional to the number of unknowns.