Scalable Solvers for Cone Complementarity Problems in Frictional Multibody Dynamics

We present an efficient, hybrid MPI/OpenMP framework for the cone complementarity formulation of large-scale rigid body dynamics problems with frictional contact. Data is partitioned among MPI processes using a Morton encoding in order to promote data locality and minimize communication. We parallelize the state-of-the-art first and second-order solvers for the resulting cone complementarity optimization problems. Our approach is highly scalable, enabling the solution of dense, large-scale multibody problems; a sedimentation simulation involving 256 million particles ($\sim 324$ million contacts on average) was resolved using 512 cores in less than half-hour per time-step.

[1]  Mihai Anitescu,et al.  A computational study of the use of an optimization-based method for simulating large multibody systems , 2009, Optim. Methods Softw..

[2]  Andreas Nüchter,et al.  Collision detection between point clouds using an efficient k-d tree implementation , 2015, Adv. Eng. Informatics.

[3]  Stephan Mertens,et al.  Random numbers for large scale distributed Monte Carlo simulations , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Timothy M. Chan.  Closest-point problems simplified on the RAM , 2002, SODA '02.

[5]  Michael J. Todd,et al.  Self-Scaled Barriers and Interior-Point Methods for Convex Programming , 1997, Math. Oper. Res..

[6]  David Gorsich,et al.  Tensor Train Accelerated Solvers for Nonsmooth Rigid Body Dynamics , 2018, Applied Mechanics Reviews.

[7]  Dan Negrut,et al.  A comparison of numerical methods for solving multibody dynamics problems with frictional contact modeled via differential variational inequalities , 2017 .

[8]  Mihai Anitescu,et al.  Using Krylov subspace and spectral methods for solving complementarity problems in many‐body contact dynamics simulation , 2013 .

[9]  Y. Nesterov.  A method for solving the convex programming problem with convergence rate O(1/k^2) , 1983 .

[10]  Tamara G. Kolda,et al.  An overview of the Trilinos project , 2005, TOMS.

[11]  Xiaoye S. Li,et al.  An overview of SuperLU: Algorithms, implementation, and user interface , 2003, TOMS.

[12]  Mihai Anitescu,et al.  An iterative approach for cone complementarity problems for nonsmooth dynamics , 2010, Comput. Optim. Appl..

[13]  Dan Negrut,et al.  Compliant contact versus rigid contact: A comparison in the context of granular dynamics. , 2017, Physical review. E.

[14]  Stefan Pirker,et al.  Hybrid parallelization of the LIGGGHTS open-source DEM code , 2015 .

[15]  Hammad Mazhar,et al.  Using Nesterov's Method to Accelerate Multibody Dynamics with Friction and Contact , 2015, ACM Trans. Graph..

[16]  Hammad Mazhar,et al.  CHRONO: a parallel multi-physics library for rigid-body, flexible-body, and fluid dynamics , 2013 .

[17]  Mihai Anitescu,et al.  Solving Large Multibody Dynamics Problems on the GPU , 2012 .

[18]  Mihai Anitescu,et al.  Optimization-based simulation of nonsmooth rigid multibody dynamics , 2006, Math. Program..

[19]  M. Anitescu,et al.  Formulating Dynamic Multi-Rigid-Body Contact Problems with Friction as Solvable Linear Complementarity Problems , 1997 .

[20]  D. Stewart,et al.  AN IMPLICIT TIME-STEPPING SCHEME FOR RIGID BODY DYNAMICS WITH INELASTIC COLLISIONS AND COULOMB FRICTION , 1996 .

[21]  M. Anitescu,et al.  A Convex Complementarity Approach for Simulating Large Granular Flows , 2010 .

[22]  Hammad Mazhar,et al.  Parallel Computing in Multibody System Dynamics: Why, When, and How , 2014 .