An h-hierarchical adaptive procedure for the scaled boundary finite-element method

The scaled boundary nite-element method (a novel semi-analytical method for solving linear partial di erential equations) involves the solution of a quadratic eigenproblem, the computational expense of which rises rapidly as the number of degrees of freedom increases. Consequently, it is desirable to use the minimum number of degrees of freedom necessary to achieve the accuracy desired. Stress recovery and error estimation techniques for the method have recently been developed. This paper describes an h-hierarchical adaptive procedure for the scaled boundary nite-element method. To allow full advantage to be taken of the ability of the scaled boundary nite-element method to model stress singularities at the scaling centre, and to avoid discretization of certain adjacent segments of the boundary, a sub-structuring technique is used. The e ectiveness of the procedure is demonstrated through a set of examples. The procedure is compared with a similar h-hierarchical nite element procedure. Since the error estimators in both cases evaluate the energy norm of the stress error, the computational cost of solutions of similar overall accuracy can be compared directly. The examples include the rst reported direct comparison of the computational e ciency of the scaled boundary nite-element method and the nite element method. The scaled boundary nite-element method is found to reduce the computational e ort considerably