HYBRID LINEAR AND QUADRATIC FINITE ELEMENT MODELS FOR 3D HELMHOLTZ PROBLEMS

In this paper, linear and quadratic finite element models are devised for the three- dimensional Helmholtz problem by using a hybrid variational functional. In each element, contin- uous and discontinuous Helmholtz fields are defined with their equality enforced over the element boundary in a weak sense. The continuous field is based on the C° nodal interpolation and the discontinuous field can be condensed before assemblage. Hence, the element can readily be in- corporated seamlessly into the standard finite element program framework. Discontinuous fields constructed by the plane-wave, Bessel and singular spherical-wave solutions are attempted. Nu- merical tests demonstrate that some of the element models are consistently and considerably more accurate than their conventional counterparts.