An effective preconditioner for wave equations

Large linear problems are ubiquitous in science and engineering. Prime examples are models of diffusion or wave propagation within complex heterogeneous materials. Iterative Krylov subspace methods tend to be used to numerically invert all but the most trivial systems. Problem-specific preconditioning transformations are often used as a catalyst for efficient convergence. Indeed, the convergence of many common methods hinges on the availability of an adequate preconditioner. 

Here, I introduce a split-preconditioning method that can be applied to a relatively broad class of non-Hermitian problems. While it proved to be effective with the most common iterative methods, it stands out for its guaranteed monotonic convergence with the Richardson iteration. The memory-efficiency of this method makes it particularly attractive for large wave problems. This enables us to solve vector-Helmholtz problems in computational domains exceeding 10⁷ cubic wavelengths.

Venue: Fulton G20