A summary of infinite element formulations for exterior Helmholtz problems

This work is devoted to a study and summary of different Infinite Element (IE) formulations for Helmholtz problems in arbitrary exterior domains. The theoretical setting for each of the different formulations is presented and related to the mathematical existence theory. The influences of a bilinear or a sesquilinear formulation are discussed as well as possible extensions to other elements. The implementation of the Infinite Element Method (IEM) incorporates the use of 2D and 3D hp Finite Elements and allows for hp-adaptive refinements. Numerical results show the computational efficiency of the coupled Finite-Infinite Element methodology