An iterative approach for cone complementarity problems for nonsmooth dynamics

Anitescu, Mihai; Tasora, Alessandro

doi:10.1007/s10589-008-9223-4

Cited by 116 publications

(147 citation statements)

References 35 publications

(69 reference statements)

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“…This results in a cone complementarity problem that can be solved with a fixed-point iteration approach, as demonstrated in our earlier work [8].…”

Section: The Overall Dynamical Modelmentioning

confidence: 92%

“…The above-mentioned limitations of the existing LCP approaches led us to develop a novel solution method based on a fixed-point iteration with projection on a convex set and presented in [8]. That method extended the seminal work on iterative LCP solvers by Mangasarian [28] to the LCP case with conical constraints, that is, a cone complementarity problem.…”

Section: Introductionmentioning

confidence: 99%

“…This extension cannot be obtained with full theoretical guarantees of convergence for the algorithm in [8] by simply replacing the bilateral constraint with two unilateral constraints. The latter case allows for unbounded internal forces, for which the approach in [8, Corollary 1] does not apply (the resulting constraint cone is not pointed).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A matrix-free cone complementarity approach for solving large-scale, nonsmooth, rigid body dynamics

Tasora

Anitescu

2011

Computer Methods in Applied Mechanics and Engineering

109

100

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This paper proposes an iterative method that can simulate mechanical systems featuring a large number of contacts and joints between rigid bodies. The numerical method behaves as a contractive mapping that converges to the solution of a cone complementarity problem by means of iterated fixed-point steps with separable projections onto convex manifolds. Since computational speed and robustness are important issues when dealing with a large number of frictional contacts, we have performed special algorithmic optimizations in order to translate the numerical scheme into a matrix-free algorithm with O(n) space complexity and easy implementation. A modified version, that can run on parallel computers is discussed. A multithreaded version of the method has been used to simulate systems with more than a million contacts with friction.

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“…This results in a cone complementarity problem that can be solved with a fixed-point iteration approach, as demonstrated in our earlier work [8].…”

Section: The Overall Dynamical Modelmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A matrix-free cone complementarity approach for solving large-scale, nonsmooth, rigid body dynamics

Tasora

Anitescu

2011

Computer Methods in Applied Mechanics and Engineering

109

100

View full text Add to dashboard Cite

show abstract

“…Most importantly, the modified scheme becomes a Cone Complementarity Problem (CCP), which can be solved efficiently by an iterative numerical method that relies on projected contractive maps. Omitting for brevity some of the details discussed in [22], the algorithm makes use of the following vectors and matrices: °i ;a´f°i;n ;°i ;u ;°i ;w g T ; i 2 A;…”

Section: The Time Stepping Solvermentioning

confidence: 99%

“…and ´i parameters are adjusted to control the convergence. Interested readers are referred to [22] for a proof of the convergence of this method.…”

Section: The Time Stepping Solvermentioning

confidence: 99%

GPU-Based Parallel Computing for the Simulation of Complex Multibody Systems with Unilateral and Bilateral Constraints: An Overview

Tasora

Negrut²,

Anitescu

2010

Computational Methods in Applied Sciences

Self Cite

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This work reports on advances in large-scale multibody dynamics simulation facilitated by the use of the Graphics Processing Unit (GPU). A description of the GPU execution model along with its memory spaces is provided to illustrate its potential parallel scientific computing. The equations of motion associated with the dynamics of large system of rigid bodies are introduced and a solution method is presented. The solution method is designed to map well on the parallel hardware, which is demonstrated by an order of magnitude reductions in simulation time for large systems that concern the dynamics of granular material. One of the salient attributes of the solution method is its linear scaling with the dimension of the problem. This is due to efficient algorithms that handle in linear time both the collision detection and the solution of the nonlinear complementarity problem associated with the proposed approach. The current implementation supports the simulation of systems with more than one million bodies on commodity desktops. Efforts are under way to extend this number to hundreds of millions of bodies on small affordable clusters.

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A computer‐aided methodology for the optimization of electrostatic separation processes in recycling

Borrotti

Pievatolo

Critelli

et al. 2015

Appl Stoch Models Bus & Ind

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The rapid growth of technological products has led to an increasing volume of waste electrical and electronic equipments (WEEE), which could represent a valuable source of critical raw materials. However, current mechanical separation processes for recycling are typically poorly operated, making it impossible to modify the process parameters as a function of the materials under treatment, thus resulting in untapped separation potentials. Corona electrostatic separation (CES) is one of the most popular processes for separating fine metal and nonmetal particles derived from WEEE. In order to optimize the process operating conditions (i.e., variables) for a given multi-material mixture under treatment, several technological and economical criteria should be jointly considered. This translates into a complex optimization problem that can be hardly solved by a purely experimental approach. As a result, practitioners tend to assign process parameters by few experiments based on a small material sample and to keep these parameters fixed during the process life-cycle. The use of computer experiments for parameter optimization is a mostly unexplored area in this field. In this work, a computer-aided approach is proposed to the problem of optimizing the operational parameters in CES processes. Three metamodels, developed starting from a multi-body simulation model of the process physics, are presented and compared by means of a numerical and simulation study. Our approach proves to be an effective framework to optimize the CES process performance. Furthermore, by comparing the predicted response surfaces of the metamodels, additional insight into the process behavior over the operating region is obtained.

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An iterative approach for cone complementarity problems for nonsmooth dynamics

Abstract: Iterative methods, Cone complementarity problems, LCP, Complementarity, Contacts, Multibody,

Cited by 116 publications

References 35 publications

A matrix-free cone complementarity approach for solving large-scale, nonsmooth, rigid body dynamics

A matrix-free cone complementarity approach for solving large-scale, nonsmooth, rigid body dynamics

GPU-Based Parallel Computing for the Simulation of Complex Multibody Systems with Unilateral and Bilateral Constraints: An Overview

A computer‐aided methodology for the optimization of electrostatic separation processes in recycling

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