Array dataow information plays an important role for successful automatic parallelization of Fortran programs. This paper proposes a pow erful symbolic array dataow analysis to support arra ypriv atizationand loop parallelization for programs with arbitrary control ow graphs and acyclic call graphs. Our scheme summarizes arra y access information using guarded array regions and propagates such regions over a Hierarchical Supergraph HSG. The use of guards allo wsus to use the information in IF conditions to sharpen the arra y datao w analysis and thereby to handle dicult cases which elude other existing techniques. The guarded array regions retain the simplicit y of set operations for regular arra yregions in common cases, and they enhance regular arra yregions in complicated cases b y using guards to handle complex symbolic expressions

Array data flow analysis is known to be crucial to the success of array privatization, one of the most important techniques for program parallelization. It is clear that array data flow analysis should be performed interprocedurally and symbolically, and that it often needs to handle the predicates represented by IF conditions. Unfortunately, such a powerful program analysis can be extremely time-consuming if not carefully designed. How to enhance the efficiency of thk analysis to a practical level remains an issue largely untouched to date. This paper documents our experience with buikling a highly efficient array data flow analyzer which is based on guarded array regions and whkh runs faster, by one or two orders of magnitude, than other similarly powerful tools.

The Riccati transfer matrix method (RTMM) improves the numerical stability of analyzing chain multibody systems with the transfer matrix method for multibody systems (MSTMM). However, for linear tree multibody systems, the recursive relations of the Riccati transfer matrices, especially those for elements with multiple input ends, have not been established yet. Thus, an RTMM formulism for general linear tree multibody systems is formulated based on the transformation of transfer equations and geometrical equations of such elements. The steady-state response under harmonic excitation of a linear tree multibody system is taken as an example and obtained by the proposed method. Comparison with the finite-element method (FEM) validates the proposed method and a numerical example demonstrates that the proposed method has a better numerical stability than the normal MSTMM.

The transfer matrix method for multibody systems is a new method with very high computational speed developed in recent 20 years for studying multibody system dynamics. By combining transfer matrix method for multibody systems, computer graphics, and open-source software, this article puts forward an approach and software MSTMMSim for visualized simulation and design of mechanical system dynamics. The approach includes the following procedures in sequence: design of functional model, design of three-dimensional solid model, design of dynamics model, automated formation of dynamics equations, and software MSTMMSim for visualized simulation and design of mechanical system dynamics. The proposed method and software provide a platform to realize the simulation and design of complex mechanical systems with the following characteristics: (1) automatic deduction of the overall transfer equation, (2) high computational speed, and (3) high visualization and programming of dynamics simulation and design process. The proposed method and software are verified by the practical example of simulation and design of a tank system dynamics using this platform. KeywordsMultibody system dynamics, transfer matrix method for multibody systems, visualized simulation and design, pre-processor, transfer matrix method for multibody system solver, post-processor, software Date

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