Modelling of short wave diffraction problems using approximating systems of plane waves

This paper describes a nite element model for the solution of Helmholtz problems at higher frequencies that o ers the possibility of computing many wavelengths in a single nite element. The approach is based on partition of unity isoparametric elements. At each nite element node the potential is expanded in a discrete series of planar waves, each propagating at a speci ed angle. These angles can be uniformly distributed or may be carefully chosen. They can also be the same for all nodes of the studied mesh or may vary from one node to another. The implemented approach is used to solve a few practical problems such as the di raction of plane waves by cylinders and spheres. The wave number is increased and the mesh remains unchanged until a single nite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced. Issues related to the integration and the conditioning are also discussed