Hybrid-Trefftz finite element models for plane Helmholtz problems

In this paper, hybrid-Trefftz four- and eight-node quadrilateral finite element models are devised for plane Helmholtz problems. In the models, independent boundary and domain approximations are defined. The former is obtained by nodal interpolation and the latter is truncated from a solution set of the Helmholtz equation. The equality of the two approximations are enforced along the element boundary thru a variational functional. Both the plane wave and Bessel solution sets are employed to construct the domain approximation. For fall rankness, a minimal of four and eight domain approximation modes are required for the four- and eight-node elements, respectively. By using local coordinates, rank sufficient and invariant elements equipped with the minimal number of approximation modes are devised. Numerical tests show that the hybrid-Trefftz elements are more accurate than their single-field counterparts.