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Review Article

TENSOR TRAIN ACCELERATED SOLVERS FOR NONSMOOTH RIGID BODY DYNAMICS

[+] Author and Article Information
Eduardo Corona

Department of Mathematics, University of Michigan
ecorona@nyit.edu

David Gorsich

U.S. Army TARDEC
david.j.gorsich.civ@mail.mil

Paramsothy Jayakumar

U.S. Army TARDEC
paramsothy.jayakumar.civ@mail.mil

Shravan Veerapaneni

Department of Mathematics, University of Michigan
shravan@umich.edu

1Corresponding author.

ASME doi:10.1115/1.4043324 History: Received August 29, 2018; Revised February 26, 2019

Abstract

In the last two decades, increased need for high-fidelity simulations of the time evolution and propagation of forces in granular media has spurred a renewed interest in the discrete element method (DEM) modeling of frictional contact. Force penalty methods, while economic and widely accessible, introduce artificial stiffness, requiring small time steps to retain numerical stability. Optimization-based methods, which enforce contacts geometrically through complementarity constraints leading to a differential variational inequality problem (DVI), allow for the use of larger time steps at the expense of solving a nonlinear complementarity problem (NCP) each time step. We review the latest efforts to produce solvers for this NCP, focusing on its relaxation to a cone complementarity problem (CCP) and solution via an equivalent quadratic optimization problem with conic constraints. We distinguish between first order methods, which use only gradient information and are thus linearly convergent and second order methods, which rely on a Newton type step to gain quadratic convergence and are typically more robust and problem-independent. However, they require the approximate solution of large sparse linear systems, thus losing their competitive advantages in large scale problems due to computational cost.

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