Additive Sweeping Preconditioner for the Helmholtz Equation
This work addresses the challenge of solving high-frequency Helmholtz equations, which is important for applications like wave propagation and scattering.
The paper introduces a new additive sweeping preconditioner for the Helmholtz equation that achieves frequency-independent iteration counts when combined with GMRES, as demonstrated in numerical examples.
We introduce a new additive sweeping preconditioner for the Helmholtz equation based on the perfect matched layer (PML). This method divides the domain of interest into thin layers and proposes a new transmission condition between the subdomains where the emphasis is on the boundary values of the intermediate waves. This approach can be viewed as an effective approximation of an additive decomposition of the solution operator. When combined with the standard GMRES solver, the iteration number is essentially independent of the frequency. Several numerical examples are tested to show the efficiency of this new approach.