TY  - EJOU
AU  - Kakuba, Godwin 
AU  - Mango, John M. 
AU  - Anthonissen, Martijn J.H. 

TI  - Convergence Properties of Local Defect Correction Algorithm for the Boundary Element Method
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2019
VL  - 119
IS  - 1
SN  - 1526-1506

AB  - Sometimes boundary value problems have isolated regions where the solution changes rapidly. Therefore, when solving numerically, one needs a fine grid to capture the high activity. The fine grid can be implemented as a composite coarse-fine grid or as a global fine grid. One cheaper way of obtaining the composite grid solution is the use of the local defect correction technique. The technique is an algorithm that combines a global coarse grid solution and a local fine grid solution in an iterative way to estimate the solution on the corresponding composite grid. The algorithm is relatively new and its convergence properties have not been studied for the boundary element method. In this paper the objective is to determine convergence properties of the algorithm for the boundary element method. First, we formulate the algorithm as a fixed point iterative scheme, which has also not been done before for the boundary element method, and then study the properties of the iteration matrix. Results show that we can always expect convergence. Therefore, the algorithm opens up a real alternative for application in the boundary element method for problems with localised regions of high activity.
KW  - Local defect
KW  -  defect correction
KW  -  composite grids
KW  -  integral equation methods
KW  -  boundary elements

DO  - 10.32604/cmes.2019.04269