Towards accuracy and scalability: Combining Isogeometric Analysis with deflation to obtain scalable convergence for the Helmholtz equation

Finding fast yet accurate numerical solutions to the Helmholtz equation remains a challenging task. The pollution error (i.e. the discrepancy between the numerical and analytical wave number k) requires the mesh resolution to be kept fine enough to obtain accurate solutions. A recent study showed that the use of Isogeometric Analysis (IgA)...

Toward a GPU-aware comparison of explicit and implicit CFD simulations on structured meshes

A computational Fluid Dynamics (CFD) code for steady simulations solves a set of non-linear partial differential equations using an iterative time stepping process, which could follow an explicit or an implicit scheme. On the CPU, the difference between both time stepping methods with respect to stability and performance has been well covered in...

Spectral analysis of the discrete Helmholtz operator preconditioned with a shifted Laplacian

Shifted Laplace preconditioners have attracted considerable attention as a technique to speed up convergence of iterative solution methods for the Helmholtz equation. In this paper we present a comprehensive spectral analysis of the Helmholtz operator preconditioned with a shifted Laplacian. Our analysis is valid under general conditions. The...

On a class of preconditioners for solving the Helmholtz equation