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

作　　者：Q.H.Zhang K.Y.Sze 

机构地区：[1]Guangdong Province Key Laboratory of Computational Science,Sun Yat-Sen University [2]Department of Mechanical Engineering,The University of Hong Kong,Pokfulam

出　　处：《Acta Mechanica Solida Sinica》2013年第6期603-618,共16页固体力学学报（英文版）

基　　金：The support of Hong Kong Research Grant Council in the form of the GRF grant HKU 7167/08E

摘　　要：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.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.

关 键 词：finite element HYBRID HELMHOLTZ BESSEL PLANE-WAVE spherical-wave radial basis function 

分 类 号：O302[理学—力学]