A parallel logarithmic time complexity algorithm for the simulation of general multibody system dynamics

Abstract

The new parallel method of Recursive Coordinate Reduction Parallelism (RCRP) is systematically derived as a special case of the fastest serial processor algorithm and outperforms existing methods both theoretically and in practice. The method is validated in an object oriented multi-threaded implementation which utilizes shared memory in a parallel computer.

To address a lack of performance with respect to general systems and modest computer resources, a new parallel algorithm of optimal order is introduced which draws exclusively from the latest developments in serial processor low order constrained system solutions. The existing constraint solution termed Recursive Coordinate Reduction (RCR) is shown to be applicable only to a narrow class of kinematic constraints and a completely generalized form is derived and verified.

Existing parallel multibody simulation methods are shown to exhibit one or more undesirable characteristics when applied to general systems. Commonly, non-optimal growth in complexity (high order) of a solution algorithm occurs. There is one existing optimal order method capable of treating general systems, but this method should only be used in conjunction with very large parallel computers, requiring currently unrealistic interprocessor communications costs to be effective.

Multibody systems encompass a vast array of machines, vehicles, and mechanisms, including molecular, bio-mechanical, and microjnano electro-mechanical systems. The ability to rapidly compute the dynamics of multibody systems is of paramount importance to technologies including real-time operator or hardware in the loop sim ulation, model based control, and comprehensive design optimization. This dissertation surveys the literature as it pertains to increased computational performance of multibody dynamics simulation and analysis, and presents and validates a novel method for achieving new levels of performance with parallel computers.