An adaptive domain of influence for element-free Galerkin method

This paper explores the feasibility of varying and adapting the sizes of the domain of influence (DOI) and the integration cells based on the nodal density in order to minimize error and to improve the efficiency of EFGM. In 2D problems, the entire problem domain is subdivided into a network of triangular cells, exploiting nodes as vertices. Thus, the size of integration cells can be adapted to the nodal density in any region while the number of integration points in all integration cells is fixed. To maintain good numerical conditioning of the system of algebraic equations, the DOI of any node must be varied to ensure that n(p) layers of cells surrounding the associated node are covered, where np is the order of the basis function. Numerical tests confirm that the proposed scheme performs effectively.