Advances in the Application of the Divide-and-Conquer Algorithm to Multibody System Dynamics

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Jeremy J. Laflin ◽  
Kurt S. Anderson ◽  
Imad M. Khan ◽  
Mohammad Poursina
Keyword(s):  
Computational Complexity ◽  
Task Scheduling ◽  
Constrained Systems ◽  
Divide And Conquer ◽  
Mathematical Framework ◽  
Complete Understanding ◽  
Basic Algorithm ◽  
Flexible Bodies ◽  
Divide And Conquer Algorithm ◽  
Serial Task

This paper summarizes the various recent advancements achieved by utilizing the divide-and-conquer algorithm (DCA) to reduce the computational burden associated with many aspects of modeling, designing, and simulating articulated multibody systems. This basic algorithm provides a framework to realize O(n) computational complexity for serial task scheduling. Furthermore, the framework of this algorithm easily accommodates parallel task scheduling, which results in coarse-grain O(log n) computational complexity. This is a significant increase in efficiency over forming and solving the Newton–Euler equations directly. A survey of the notable previous work accomplished, though not all inclusive, is provided to give a more complete understanding of how this algorithm has been used in this context. These advances include applying the DCA to constrained systems, flexible bodies, sensitivity analysis, contact, and hybridization with other methods. This work reproduces the basic mathematical framework for applying the DCA in each of these applications. The reader is referred to the original work for the details of the discussed methods.

New and Extended Applications of the Divide-and-Conquer Algorithm for Multibody Dynamics

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Jeremy J. Laflin ◽  
Kurt S. Anderson ◽  
Imad M. Khan ◽  
Mohammad Poursina
Keyword(s):  
Multibody Dynamics ◽  
Large Deformations ◽  
Multibody System ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Ongoing Research ◽  
Flexible Bodies ◽  
Computational Burden ◽  
Divide And Conquer Algorithm ◽  
Model Fidelity

This work presents a survey of the current and ongoing research by the authors who use the divide-and-conquer algorithm (DCA) to reduce the computational burden associated with various aspects of multibody dynamics. This work provides a brief discussion of various topics that are extensions of previous DCA-based algorithms or novel uses of this algorithm in the multibody dynamics context. These topics include constraint error stabilization, spline-based modeling of flexible bodies, model fidelity transitions for flexible-body systems, and large deformations of flexible bodies. It is assumed that the reader is familiar with the “Advances in the Application of the DCA to Multibody System Dynamics” text as the notation used in this work is explained therein and provides a summary of how the DCA has been used previously.

Extended Divide-and-Conquer Algorithm for Uncertainty Analysis of Multibody Systems in Polynomial Chaos Expansion Framework

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Mohammad Poursina
Keyword(s):  
Computational Complexity ◽  
Polynomial Chaos ◽  
Equations Of Motion ◽  
Divide And Conquer ◽  
Chaos Expansion ◽  
Entire System ◽  
Governing Equations ◽  
Divide And Conquer Algorithm ◽  
Base Functions ◽  
Modal Values

In this paper, an advanced algorithm is presented to efficiently form and solve the equations of motion of multibody problems involving uncertainty in the system parameters and/or excitations. Uncertainty is introduced to the system through the application of polynomial chaos expansion (PCE). In this scheme, states of the system, nondeterministic parameters, and constraint loads are projected onto the space of specific orthogonal base functions through modal values. Computational complexity of traditional methods of forming and solving the resulting governing equations drastically grows as a cubic function of the size of the nondeterministic system which is significantly larger than the original deterministic multibody problem. In this paper, the divide-and-conquer algorithm (DCA) will be extended to form and solve the nondeterministic governing equations of motion avoiding the construction of the mass and Jacobian matrices of the entire system. In this strategy, stochastic governing equations of motion of each individual body as well as those associated with kinematic constraints at connecting joints are developed in terms of base functions and modal terms. Then using the divide-and-conquer scheme, the entire system is swept in the assembly and disassembly passes to recursively form and solve nondeterministic equations of motion for modal values of spatial accelerations and constraint loads. In serial and parallel implementations, computational complexity of the method is expected to, respectively, increase as a linear and logarithmic function of the size.

scholarly journals A divide-and-conquer algorithm for quantum state preparation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Israel F. Araujo ◽  
Daniel K. Park ◽  
Francesco Petruccione ◽  
Adenilton J. da Silva
Keyword(s):  
Computational Cost ◽  
Quantum Circuit ◽  
Divide And Conquer ◽  
Computational Time ◽  
Quantum Computers ◽  
Dimensional Vector ◽  
Quantum Devices ◽  
Divide And Conquer Algorithm ◽  
Quantum State Preparation ◽  
Quantum Device

AbstractAdvantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O(N) to load an N-dimensional vector. Here, we show that it is possible to load an N-dimensional vector with exponential time advantage using a quantum circuit with polylogarithmic depth and entangled information in ancillary qubits. Results show that we can efficiently load data in quantum devices using a divide-and-conquer strategy to exchange computational time for space. We demonstrate a proof of concept on a real quantum device and present two applications for quantum machine learning. We expect that this new loading strategy allows the quantum speedup of tasks that require to load a significant volume of information to quantum devices.

Influence and Information Flow in Online Social Networks

2017 ◽  
Vol 9 (4) ◽  
pp. 1-17
Author(s):  
Afrand Agah ◽  
Mehran Asadi
Keyword(s):  
Social Networks ◽  
Online Social Networks ◽  
Large Data ◽  
Marketing Strategies ◽  
Large Data Sets ◽  
Divide And Conquer ◽  
Data Sets ◽  
Divide And Conquer Algorithm ◽  
Flow Of Information

This article introduces a new method to discover the role of influential people in online social networks and presents an algorithm that recognizes influential users to reach a target in the network, in order to provide a strategic advantage for organizations to direct the scope of their digital marketing strategies. Social links among friends play an important role in dictating their behavior in online social networks, these social links determine the flow of information in form of wall posts via shares, likes, re-tweets, mentions, etc., which determines the influence of a node. This article initially identities the correlated nodes in large data sets using customized divide-and-conquer algorithm and then measures the influence of each of these nodes using a linear function. Furthermore, the empirical results show that users who have the highest influence are those whose total number of friends are closer to the total number of friends of each node divided by the total number of nodes in the network.

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