Massively parallel computational methods for finite element analysis of transient structural responses

Abstract

With the emphasis on the finitely damped system (e.g. control structure interaction) case, two fully implicit and two semi-implicit sets of finite element method-based numerical algorithms are formulated for transient response analysis of space frame and truss structures in a massively parallel processing (MPP) environment. All algorithm sets use an implicit force calculation/vector equation of motion assembly procedure. The semi-implicit algorithms are based on the explicit central difference (CD) and the fourth-order Runge-Kutta (RK4) schemes, respectively, in conjunction with the use of mass lumping techniques so that solution of the recurrence equations for unknown displacements is reduced to a trivial diagonal matrix inversion operation. The fully implicit algorithm sets are based on the Newmark Beta (NB) and CD schemes, respectively, in conjunction with use of the (iterative) preconditioned conjugate gradient (PCG) method for solving the linear algebraic recurrence equations. The semi-implicit algorithm sets are fully implemented and assessed on an MPP CM-2 computer. A preliminary assessment of the fully implicit sets of algorithms is made on a Sun Workstation. These numerical study results show that the newly formulated MPP algorithms are, to a varying degree, superefficient (or potentially superefficient) on the CM-2 compared with, and even highly competitive against, the conventional sequential algorithms on an advanced serial computer.