A p-adaptive scaled boundary finite element method based on maximization of the error decrease rate

Abstract

This study enhances the classical energy norm based adaptive procedure by introducing new refinement criteria, based on the projection-based interpolation technique and the steepest descent method, to drive mesh refinement for the scaled boundary finite element method. The technique is applied to p-adaptivity in this paper, but extension to h-and hp-adaptivity is straightforward. The reference solution, which is the solution of the fine mesh formed by uniformly refining the current mesh, is used to represent the unknown exact solution. In the new adaptive approach, a projection-based interpolation technique is developed for the 2D scaled boundary finite element method. New refinement criteria are proposed. The optimum mesh is assumed to be obtained by maximizing the decrease rate of the projectionbased interpolation error appearing in the current solution. This refinement strategy can be interpreted as applying the minimisation steepest descent method. Numerical studies show the new approach out-performs the conventional approach.

A coupled BEM/scaled boundary FEM formulation for accurate computations in linear elastic fracture mechanics

“…Consequently, ill-conditioned systems of the order 13 10 , such as found by selecting 1  in both analytical verification examples, were solved to the same level of accuracy as those with 6 10  . However, should the method be written without such solvers, care should be taken to avoid ill-conditioning by selecting an appropriate scaling factor, such that the terms in the influence matrices, H and G , are of the same order of magnitude.…”

“…This stress recovery technique and error estimator was used in conjunction with an h-hierarchical procedure to develop a simple h-adaptive mesh refinement strategy [12]. Vu and Deeks later developed a p-adaptive refinement procedure and showed that higher order shape functions in this adaptive technique offered improved convergence over h-adaptive methods [13,14]. Deeks developed a method of prescribing Dirichlet boundary conditions (displacement constraints) along side faces [15] and also demonstrated that the use of linear elements can give higher-order results on the undiscretised side faces.…”

Scaled boundary finite element method with circular defining curve for geo-mechanics applications

“…This work was applied to a number of standard linear elasticity problems, and the technique was found to offer higher and better convergence than the original SBFEM. Furthermore, Vu and Deeks [11] presented a p-adaptive in the SBFEM for the two dimensional problem. These authors investigated an alternative set of refinement criteria.…”

Scaled Boundary Finite Element Method for Two-Dimensional Linear Multi-Field Media

“…Although, the SBFEM has been successfully implemented in various applications, it also possesses certain drawbacks when the number of degrees of freedom resulting from the discretization becomes large, rendering the computational expenses substantial. To overcome such disadvantage, Vu and Deeks [30] integrated a p-adaptive scheme in the SBFEM for solving two dimensional boundary value problems. In this study, an alternative set of refinement criteria was considered to maximize the solution accuracy while minimizing the computational cost.…”