Subgrid modeling in a Galerkin method for the Helmholtz equation Original Research Article

We improve the accuracy of finite element acoustic wave solutions without introducing additional degrees of freedom with physically inspired subgrid models. The models explored here will not adversely impact system matrix storage or bandwidth, can be used for structured or unstructured meshes, do not require the solution of any auxiliary value problems, and have minimal marginal overall computational cost. One interpretation of the new models is as momentum transferred to and from ‘modes’ at length scales below the local mesh dimension. We show a method to approximate the effects of all subgrid modes on the grid scale solution, and the significant improvements in local accuracy that the new models provide. The new subgrid models also improve global or ‘pollution’ accuracy through a reduction in the element dispersion error. In addition, we draw comparisons between this proposed method and much of the alternative and related work in this area.