Abstract
An algebraic multigrid (AMG) with aggregation technique to coarsen is applied to construct a better preconditioner for solving Helmholtz equations in this paper. The solution process consists of constructing the preconditioner by AMG and solving the preconditioned Helmholtz problems by Krylov subspace methods. In the setup process of AMG, we employ the double pairwise aggregation (DPA) scheme firstly proposed by Y. Notay (2006) as the coarsening method. We compare it with the smoothed aggregation algebraic multigrid and meanwhile show shifted Laplacian preconditioners. According to numerical results, we find that DPA algorithm is a good choice in AMG for Helmholtz equations in reducing time and memory. Spectral estimation of system preconditioned by the three methods and the influence of second‐order and fourth‐order accurate discretizations on the three techniques are also considered.
Highlights
In this paper, the time-harmonic wave equation in 2D homogeneous media is solved numerically
The reason is that the high wavenumber is able to make the corresponding matrices of Helmholtz equations highly indefinite
We consider using the algebraic multigrid method to construct the preconditioner and look for a concrete AMG method which is fit for Helmholtz problems
Summary
The time-harmonic wave equation in 2D homogeneous media is solved numerically. We consider an algebraic multigrid with aggregation scheme as preconditioning to improve the convergence of Krylov subspace iterative methods. In 2007, Airaksinen et al 8 proposed a preconditioner based on an algebraic multigrid approximate of the inverse of a shifted Laplacian for the Helmholtz equation. This is a generalization of the preconditioner proposed by Erlangga et al in 5. We will consider using the double pairwise aggregation algorithm to coarsen in the setup process of the general algebraic multigrid method in this paper in order to improve the solution effects of Helmholtz problems.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
