Numerical p-version refinement studies for the regularized stress-BEM

In the development of the boundary element method (BEM) and the nite element method (FEM) researchers have typically selected similar basis functions. That is, both methods typically employ loworder interpolations such as piece-wise linear or piece-wise quadratic and rely on h-version re nement to increase accuracy as required. In the case of the FEM, the decision to use low-order elements is made for computational e ciency as an attractive compromise between local modeling accuracy and sparseness of the resulting linear system. However, in many BEM formulations, low-order elements may be the only practical choice given the complexity of using analytic integration formul in conjunction with special integral interpretations. Unlike their e cient use in the FEM, ne meshes of low-order elements in the BEM are highly ine cient from a computational standpoint given the dense nature of BEM systems. Moreover, owing to singularities in the kernel functions, the BEM should be expected to bene t more so than the FEM from very high levels of local accuracy. Through the use of regularized algorithms which only require numerical integration, p-version re nement in the BEM is easily extended to include any set of basis functions with no signi cant increase in programming complexity. Numerical results show that by using interpolations as high as 12th and 16th order, one can expect reductions in error by as many as ve orders of magnitude over comparable algorithms based on similar system size. For two-dimensional problems, it is also shown that, for a given level of error, one can expect reductions in system size by an order of magnitude, thus leading to a reduction in computational expense for conventional algorithms by three orders of magnitude