Description:
When simulating acoustic, elastodynamic, or coupled fluid-solid vibration problems using standard finite element (FE) techniques, several elements per wavelength are needed to obtain a tolerable accuracy for engineering purposes. At high wave numbers, the requirement of dense meshes may lead to an overwhelmingly large computational burden, which significantly limits the feasibility of FE methods for the modeling of wave phenomena. A promising technique for reducing the computational complexity is to use plane wave basis functions opposed to the low-order polynomials that are used in conventional FE methods. A possible method for utilizing the plane wave basis is the ultra-weak variational formulation (UWVF). The UWVF method can be used for acoustic Helmholtz problems, elastodynamic Navier problems, or fluid-solid systems characterized by a coupled Helmholtz-Navier model. A comparison of the UWVF technique with a low-order FE method shows reduced computational complexity and improved accuracy.