Stress-intensity factors (SIFs) are the most important parameters in fracture mechanics analysis of structures. These parameters are evaluated for a stationary crack in functionally graded plates of arbitrary geometry using a novel Galerkin based mesh-free method. The method involves an element-free Galerkin method (EFGM), where the material properties are smooth functions of spatial coordinate...

To solve crack problems, some coupled methods have been developed in recent years. Most of these methods have some shortcomings such as the need for a transition region. The finite element and enriched element free Galerkin methods are widely used for this class of problems. In order to take the advantages of these methods while avoiding the disadvantages, it is essential to follow solution app...

The aim of the present paper is to formalize semantic-directed lexical selection by virtue of frame-based semantic inference capability built in the CFL representation language. The DG model of paraphrasing semantic descriptions can explicate logical process of knowledge-based sentence generation excluding any particular procedures for lexical selection or syntax structure generation. In additi...

In this paper, we develop the locally divergence-free discontinuous Galerkin method for numerically solving the Maxwell equations. The distinctive feature of the method is the use of approximate solutions that are exactly divergence-free inside each element. As a consequence, this method has a smaller computational cost than that of the discontinuous Galerkin method with standard piecewise poly...

The e ciency of the quadrature-free form of the discontinuous Galerkin method in two dimensions, and brie y in three dimensions, is examined. Most of the work for constant-coe cient, linear problems involves the volume and edge integrations, and the transformation of information from the volume to the edges. These operations can be viewed as matrix-vector multiplications. Many of the matrices a...