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, continuous 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 C⁰ nodal interpolation and the discontinuous field can be condensed before assemblage. Hence, the element can readily be incorporated seamlessly into the standard finite element program framework. Discontinuous fields constructed by the plane-wave, Bessel and singular spherical-wave solutions are attempted. Numerical tests demonstrate that some of the element models are consistently and considerably more accurate than their conventional counterparts.