A knowledge-based system for the determination of activity indicators for self-adaptive grid methods

Many important physical problems exhibit phenomena that require local grid resolution. Activity indicators are used by local grid refinement schemes to determine where to place or remove local grids, in order to achieve a better accuracy on the numerical procedure. We present a methodology for the selection of activity indicators and show how to automate the process using a knowledge-based system that adjusts its parameters based on its previous experiences with similar problems. The methodology is: a class of model problems is constructed; then we specify the set of relevant parameters to be used in the quantification of the results obtained when solving a problem with a particular indicator. A database is created to maintain all the parameters used in the quantification process, as well as the particular scores for each indicator. For each problem, the database is updated and the total scores are modified to reflect the new experience. As the number of problems considered increases, the scores in the database will stabilize providing information about the relative “goodness” of each indicator.