The effect of discretization and boundary conditions on the convergence rate of the dynamic relaxation method

The Dynamic Relaxation (DR) method is a robust iterative solver for highly nonlinear finite element problems. It is particularly useful where the large number of degrees of freedom, or sliding contact, require an explicit formulation to avoid excessive memory requirements. Although the DR method converges consistently, the convergence rate is sometimes slower than desired. Experience gained in using DR has led to some general principles in the finite element discretization, to optimize the convergence rate. Two distinct features of the discretization are the relative size of adjacent elements, and the method of supporting the body at boundaries. Theoretical bases for the influence of these features on convergence rate is presented. A systematic study of the effect of varying the ratio of neighbouring element size shows that, in general, abrupt changes in element size can significantly slow the convergence rate. Also, the use of alternative boundary constraints to minimize translation of the most refined portion of the mesh can have a dramatic effect on convergence rate.