Parallel processing of 3D rigid-plastic finite element method using diagonal matrix

To enable large-scale 3D simulation of metal forming processes, the 3D rigid-plastic finite element method using a diagonal matrix is extended to parallel processing. In the present method, uncoupled equilibrium equations expressed by a matrix with three rows and three columns at each nodal point are repeatedly calculated in turn without solving the large global simultaneous equations. The method using a diagonal matrix is suitable for parallel processing because of the iterative calculation at each nodal point. The convergence of the solution is examined in the simulation of upsetting of a rectangular block with an inclined tool. The speedup of the computation in the parallel processing considerably approaches the ideal one using the odd–even method in the nodal point assignment approach and the intermittent correction of non-linearity in equilibrium equations. It is found that the present parallel method is suitable for the large-scale three-dimensional simulation of metal forming processes.