Vectorization (mathematics)

Abstract: The reconstruction of noisy digital shapes is a complex question and a lot of contributions have been proposed to address this problem , including blurred segment decomposition or adaptive tangential covering for instance In this article, we propose a novel approach combining multi-scale and irregular isothetic representations of the input contour, as an extension of a previous work [Vacavant et al, A Combined Multi-Scale/Irregular Algorithm for the Vectorization of Noisy Digital Contours , CVIU 2013] Our new algorithm improves the representation of the contour by 1-D intervals, and achieves afterwards the decomposition of the contour into maximal arcs or segments Our experiments with synthetic and real images show that our contribution can be employed as a relevant option for noisy shape reconstruction

Abstract: Contact-impact algorithms, which are sometimes called slideline algorithms, are a computationally time-consuming part of many explicit simulations of non-linear problems because they involve many branches, so they are not amenable to vectorization, which is essential for speed on supercomputers. The pinball algorithm is a simplified slideline algorithm which is readily vectorized. Its major idea is to embed pinballs in surface elements and to enforce the impenetrability condition only to pinballs. It can be implemented in either a Lagrange multiplier or penalty method. It is shown that, in any Lagrange multiplier method, no iterations are needed to define the contact surface. Examples of solutions and running times are given.

Abstract: The general chemical dynamics computer program VENUS is used to perform classical trajectory simulations for large polyatomic systems, with many atoms and complicated potential energy functions. To simulate an ensemble of many trajectories requires a large amount of CPU time. Since each trajectory is independent, it is possible to parallel process a large set of trajectories instead of processing the trajectories by the conventional sequential approach. This enhances the vectorizability of the VENUS program, since the integration of Hamilton's equations of motion and the gradient evaluation, which comprise 97.8% of the CPU, can each be parallel processed. In this article, the vectorization and ensuing optimization of VENUS on the CRAY‐YMP and IBM‐3090 are presented in terms of both global strategies and technical details. A switching algorithm is designed to enhance the vector performance and to minimize the memory storage. A performance of 140 MFLOPS and a vector/scalar execution rate ratio of 10.6 are observed when this new version of VENUS is used to study the association of CH3 with the H(Ar)12 cluster on the CRAY‐YMP.