High order isoparametric elements in boundary element method—Smooth spheroidal element

Abstract

The smooth spheroidal element, a high order isoparametric element, is constructed and applied in the boundary element method (BEM) for modeling closed surface of spheroid as well as the field variables using a single element. The smoothness of the element is realized by repeated use of real nodes as auxiliary nodes of interpolation along both the latitude and meridian directions to remove the end node/line effects existing in the conventional closure element. The special techniques of shape function manipulations are suggested and presented to deal with the integrals with hyper- or near hyper-singularities in a uniform and simple way encountered in the BEM. A combined technique, the distance transformation with possible subdivision is proposed to improve the evaluation of near singular integrals. Through a number of numerical examples, the accuracy and efficiency of using high order smooth elements are demonstrated by checking the fitting accuracy of geometrical parameters, the computation costs and some bench mark tests in elasticity.