Abstract: The stationing situation's effect on error in the single domain of influence in element-free method (EFM) is studied. The idea of radius's weight has been presented. After completely numerical computing, the magnitude of influence on the accuracy of the EFM's interpolation result can be presented. The study can optimize the stationing situation of EFM, minimize the simulation errors; and the effect that the domain of influence does not depend on the number of the nodes can avoid the disadvantages of the oversize domain of influence and extra numbers of the whole interpolation nodes which is resulted from maintaining the enough interpolation nodes in single domain of influence. Then the paper also apply this theory of the stage of health in single domain for the work that take the distributing point effect on the simulation precision of MLSM which is the function EFM. The genetic algorithm is used to optimize the interpolating points; and the optimizing values are given. With an example, the relation between the optimizing value of interpolating points that have a general significance are obtained; and the density of interpolating points following with the universal principle of distribution point in element-free method.

Key words: EFM, degree of health, domain of influence, genetic algorithms, encoding fitness, selection strategy, genetic operator