Convergence properties of local defect correction algorithm for the boundary element method

Godwin Kakuba (Corresponding author), John M. Mango, Martijn J.H. Anthonissen

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
11 Downloads (Pure)

Abstract

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.

Original languageEnglish
Pages (from-to)207-225
Number of pages19
JournalComputer Modeling in Engineering and Sciences
Volume119
Issue number1
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Boundary elements
  • Composite grids
  • Defect correction
  • Integral equation methods
  • Local defect

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