Parallel Iterative Equation Solver with Multi-Point Constraint Preconditioning for Assembled Structural Analysis
Kazuya Goto · TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A · 2012
In this study, an efficient technique for satisfying multi-point constraints in the parallel conjugate gradient method is proposed. Our strategy is to eliminate the dependent degrees of freedom from the system matrix equations (Ku = f ) by using the constraint conditions (Bu = 0 ). The elimination process is implemented in the conjugate gradient solver in such a way that the “MPC preconditioning matrix” is multiplied at each iteration step. In addition, a preconditioning based on the system matrix without multi-point constraints is introduced. The proposed method was implemented in a parallel finite element structural analysis software and its performance was measured. In a practical example problem with over one million degrees of freedom, both the number of iterations and computational time for convergence were reduced by about 94% compared to the penalty method. Parallel performance was also measured and 7.7 times speed-up was achieved with eight MPI processes. The result shows the effectiveness of the proposed method against large-scale assembled structural analyses.