Model Transitions and Optimization Problem in Multi-Flexible-Body Modeling of Biopolymers

2011 ◽  
Author(s):  
Mohammad Poursina ◽  
Imad Khan ◽  
Kurt S. Anderson
Keyword(s):  
Optimization Problem ◽  
Computational Cost ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Basic Form ◽  
Divide And Conquer Algorithm ◽  
Time Optimal ◽  
Logarithmic Complexity ◽  
Algorithm Implementation ◽  
Fidelity Model

This paper presents an efficient algorithm for the simulation of multi-flexible-body systems undergoing discontinuous changes in model definition. The equations governing the dynamics of the transitions from a higher to a lower fidelity model and vice versa are formulated through imposing/removing certain constraints on/from the system. Furthermore, the issue of the non-uniqueness of the results associated with the transition from a lower to a higher fidelity model is dealt with as an optimization problem. This optimization problem is subjected to the satisfaction of the impulse-momentum equations. The divide and conquer algorithm (DCA) is applied to formulate the dynamics of the transition. The DCA formulation in its basic form is time optimal and results in linear and logarithmic complexity when implemented in serial and parallel, respectively. As such, it reduces the computational cost of formulating and solving the optimization problem in the transitions to the finer models. Necessary mathematics for the algorithm implementation is developed and a numerical example is given to validate the method.

Multi-Flexible-Body Simulations Using Interpolating Splines in a Divide-and-Conquer Scheme

2013 ◽  
Author(s):  
Imad M. Khan ◽  
Woojin Ahn ◽  
Kurt Anderson ◽  
Suvranu De
Keyword(s):  
Equations Of Motion ◽  
Linear Equations ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Divide And Conquer Algorithm ◽  
Large Rotations ◽  
Floating Frame ◽  
Interpolating Splines ◽  
Divide And Conquer Scheme ◽  
Logarithmic Complexity

A new method for modeling multi-flexible-body systems is presented that incorporates interpolating splines in a divide-and-conquer scheme. This algorithm uses the floating frame of reference formulation and piece-wise interpolation spline functions to construct and solve the non-linear equations of motion of the multi-flexible-body systems undergoing large rotations and translations. We compare the new algorithm with the flexible divide-and-conquer algorithm (FDCA) that uses the assumed modes method and may resort to sub-structuring in many cases [1]. We demonstrate, through numerical examples, that in such cases the interpolating spline-based approach is comparable in accuracy and superior in efficiency to the FDCA. The algorithm retains the theoretical logarithmic complexity inherent to the divide-and-conquer algorithm when implemented in parallel.

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.

Efficient Large Deformation Simulations of Multi-Flexible-Body Systems Using Absolute Nodal Coordinate Beam and Plate Elements

2014 ◽  
Author(s):  
Imad M. Khan ◽  
Kurt S. Anderson
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Elastic Deformations ◽  
Absolute Nodal Coordinate ◽  
Numerical Examples ◽  
Divide And Conquer Algorithm ◽  
Plate Elements ◽  
The Absolute ◽  
The Individual

In this paper, we investigate the absolute nodal coordinate finite element (FE) formulations for modeling multi-flexible-body systems in a divide-and-conquer framework. Large elastic deformations in the individual components (beams and plates) are modeled using the absolute nodal coordinate formulation (ANCF). The divide-and-conquer algorithm (DCA) is utilized to model the constraints arising due to kinematic joints between the flexible components. We develop necessary equations of the new algorithm and present numerical examples to test and validate the method.

Efficient Operational Space Sensitivity Analysis of Dynamic Multibody Systems

2011 ◽  
Author(s):  
Rudranarayan M. Mukherjee
Keyword(s):  
Sensitivity Analysis ◽  
Data Storage ◽  
Multibody Systems ◽  
Parallel Implementation ◽  
Divide And Conquer ◽  
Parametric Perturbation ◽  
Divide And Conquer Algorithm ◽  
Operational Space ◽  
Tree Topologies ◽  
Logarithmic Complexity

This paper presents a generalization of the divide and conquer algorithm for sensitivity analysis of dynamic multibody systems based on direct differentiation. While similar sensitivity analysis approach has been demonstrated for multi-rigid and multi-flexible systems in tree topologies and a limited set of kinematically closed loop topologies, this paper presents the generalization of these approaches to systems in generalized topologies including many coupled kinematically closed loops. This generalization retains the efficient complexity of the underlying formulations i.e. linear and logarithmic complexity in serial and parallel implementation. Other than the computational efficiency, the advantages of this method include concurrent sensitivity analysis with forward dynamics, no numerical artifacts arising from parametric perturbation and significantly reduced data storage compared to traditional methods. An interesting application of this work in control of multibody systems is discussed.

scholarly journals A divide-and-conquer algorithm for seismic data approximation by the Laguerre series

2021 ◽  
Vol 2099 (1) ◽  
pp. 012062
Author(s):  
Andrew V Terekhov
Keyword(s):  
Seismic Data ◽  
Computational Cost ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Divide And Conquer ◽  
Data Approximation ◽  
Laguerre Transform ◽  
Divide And Conquer Algorithm ◽  
The One ◽  
Initial Boundary Value

Abstract An algorithm of the Laguerre transform for approximating functions on large intervals is proposed. The idea of the considered approach is that the calculation of improper integrals of rapidly oscillating functions is replaced by a solution of an initial boundary value problem for the one-dimensional transport equation. It allows one to successfully avoid the problems associated with the stable implementation of the Laguerre transform. A divide-and-conquer algorithm based on shift operations made it possible to significantly reduce the computational cost of the proposed method. Numerical experiments have shown that the methods are economical in the number of operations, stable, and have satisfactory accuracy for seismic data approximation.

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.

Dynamics and Control of Multi-Flexible-Body Systems in a Divide-and-Conquer Scheme

2015 ◽  
Author(s):  
Imad M. Khan ◽  
Kalyan C. Addepalli ◽  
Mohammad Poursina
Keyword(s):  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Constraint Forces ◽  
Control Laws ◽  
Motion Constraints ◽  
Divide And Conquer Algorithm ◽  
Dynamics And Control ◽  
Kinematic Loops

In this paper, we present an extension of the generalized divide-and-conquer algorithm (GDCA) for modeling constrained multi-flexible-body systems. The constraints of interest in this case are not the motion constraints or the presence of closed kinematic loops but those that arise due to inverse dynamics or control laws. The introductory GDCA paper introduced an efficient methodology to include generalized constraint forces in the handle equations of motion of the original divide-and-conquer algorithm for rigid multibody systems. Here, the methodology is applied to flexible bodies connected by kinematic joints. We develop necessary equations that define the algorithm and present a well known numerical example to validate the method.

Divide-and-Conquer-Based Large Deformation Formulations for Multi-Flexible Body Systems

2013 ◽  
Author(s):  
Imad M. Khan ◽  
Kurt S. Anderson
Keyword(s):  
Modeling And Simulation ◽  
Role Model ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Divide And Conquer ◽  
Model Complexity ◽  
Flexible Body ◽  
Elastic Bodies ◽  
Large Rotations ◽  
High Computational Cost

In the dynamic modeling and simulation of multi-flexible-body systems, large deformations and rotations has been a focus of keen interest. The reason is a wide variety of application area where highly elastic components play important role. Model complexity and high computational cost of simulations are the factors that contribute to the difficulty associated with these systems. As such, an efficient algorithm for modeling and simulation of systems undergoing large rotations and large deflections may be of great importance. We investigate the use of absolute nodal coordinate formulation (ANCF) for modeling articulated flexible bodies in a divide-and-conquer (DCA) framework. It is demonstrated that the equations of motion for individual finite elements or elastic bodies, as obtained by the ANCF, may be assembled and solved using a DCA type method. The current discussion is limited to planar problems but may easily be extended to spatial applications. Using numerical examples, we show that the present algorithm provides an efficient and robust method to model multibody systems employing highly elastic bodies.

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