Hybrid-Trefftz finite elements for Helmholtz problem

Abstract

In this paper, our work on formulating hybrid-Trefftz finite element models for Helmholtz problem is briefly reviewed. These elements are devised via a hybrid variational principle and can readily be incorporated into the standard finite element program framework. In the elements, boundary and domain Helmholtz variables are defined. The former is obtained by nodal interpolation and the latter is truncated from wave solution sets. The equality of the two approximations are enforced along the boundary. Both the plane-wave and cylindrical-wave solutions are employed to construct the domain variable. Considerations have been given to securing the robust features of the finite element models including rank sufficiency and invariance. © 2010 American Institute of Physics.