Computational Aspects of the Ultra-Weak Variational Formulation

The ultra-weak variational formulation (UWVF) approach has been proposed as an effective method for solving Helmholtz problems with high wave numbers. However, for coarse meshes the method can suffer from instability. In this paper we consider computational aspects of the ultra-weak variational formulation for the inhomogeneous Helmholtz problem. We introduce a method to improve the UWVF scheme and we compare iterative solvers for the resulting linear system. Computations for the acoustic transmission problem in 2D show that the new approach enables Helmholtz problems to be solved on a relatively coarse mesh for a wide range of wave numbers.