Local defect correction for boundary integral equation methods

This paper presents a new approach to gridding for problems with localised regions of high activity. The technique of local defect correction has been studied for other methods as finite difference methods and finite volume methods. In this paper we develop the technique for the boundary element method, an integral equation method. The technique offers an iterative way for obtaining the solution on an equivalent composite grid. It uses two grids: a global uniform coarse grid covering the whole boundary and a local fine grid covering the local active boundary. The solution of the local problem on the local fine grid is used to estimate the defect on the fine grid. The defect is then added to the right hand side of the global coarse grid problem which is then solved again to obtain a better updated solution. We demonstrate the technique’s strength using an example and show that it offers a cheaper alternative to either solving on a global uniform grid or directly on a composite grid.