An element-by-element iteration procedure for the solution of discrete algebraic systems of DQ-related discrete element analysis methods

In recent years, some new DQ-related discrete element analysis methods were proposed by the present author. These methods are DQEM, DQFEM, DQFDM, GDQEM and GCDQEM. The performance of these numerical methods is excellent. Moreover, they have the advantage of bing suitable to consistently discretize continuum mechanics problems having arbitrarily complex geometries. They are all suitable for vector and parallel processing. In this paper, an element-by-element iteration procedure is proposed for solving the resulting discrete algebraic systems of DQ-related discrete element analysis methods. Instead of solving the assembled overall discrete algebraic systems from the DQrelated discrete element analysis methods, the solution of discrete algebraic systems can be carried out using an element-by-element iteration procedure. By using this computational procedure, the largest computation system for solving a discrete algebraic system is an element-basis. The kinematic transition conditions and natural transition conditions are used to carry out the iterative solution from one element to the next one. This iterative computation procedure is effective.