A nonrecursive order N preconditioned conjugate gradient: Range space formulation of MDOF dynamics

摘要

While excellent progress has been made in deriving algorithms that are efficient for certain combinations of system topologies and concurrent multiprocessing hardware, several issues must be resolved to incorporate transient simulation in the control design process for large space structures. Specifically, strategies must be developed that are applicable to systems with numerous degrees of freedom. In addition, the algorithms must have a growth potential in that they must also be amenable to implementation on forthcoming parallel system architectures. For mechanical system simulation, this fact implies that algorithms are required that induce parallelism on a fine scale, suitable for the emerging class of highly parallel processors; and transient simulation methods must be automatically load balancing for a wider collection of system topologies and hardware configurations. These problems are addressed by employing a combination range space/preconditioned conjugate gradient formulation of multi-degree-of-freedom dynamics. The method described has several advantages. In a sequential computing environment, the method has the features that: by employing regular ordering of the system connectivity graph, an extremely efficient preconditioner can be derived from the 'range space metric', as opposed to the system coefficient matrix; because of the effectiveness of the preconditioner, preliminary studies indicate that the method can achieve performance rates that depend linearly upon the number of substructures, hence the title 'Order N'; and the method is non-assembling. Furthermore, the approach is promising as a potential parallel processing algorithm in that the method exhibits a fine parallel granularity suitable for a wide collection of combinations of physical system topologies/computer architectures; and the method is easily load balanced among processors, and does not rely upon system topology to induce parallelism.