The Rensselaer Polytechnic Institute Computational Dynamics Laboratory 1102022

The Rensselaer Polytechnic Institute Computational Dynamics Laboratory 1/10/2022 Rensselaer Computational Dynamics Laboratory 1

Who are We? • Faculty Professor Kurt S. Anderson • Graduate Students Rudranarayan Mukherjee Kishor Bhalerao Mohammad Poursina 1/10/2022 Rensselaer Computational Dynamics Laboratory 2

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• Rudranarayan Mukherjee, Ph. D Student • Focus: Evaluation of parallel algorithms for applicability to protein folding and macro molecular dynamics • Past Researchers – – – Shanzhong Duan, Ph. D. Yu. Hung Hsu, Ph. D. Omer Gundogdu, Ph. D. Jason Rosner, MS Philip Stephanou, MS 1/10/2022 Rensselaer Computational Dynamics Laboratory 5

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What Do We Do? • A Unified Approach Bridging the Gap Between Dynamics, Computer Science, and Numerics • Recursive Coordinate Reduction RCR Parallelism and Application to Unilateral Constraints • State-Time Dynamic Formulation State-of-the-Art Dynamic Formulation with the Aim of Massively Parallel Computing 1/10/2022 Rensselaer Computational Dynamics Laboratory 7

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Note: n= Number of System Generalized Coordinates, m = Number of System Constraints 1/10/2022 Rensselaer Computational Dynamics Laboratory 9

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Multi-Scale Multibody Dynamics Hierarchic Multi-resolution Substructured Model Articulated Rigid Body Model – Coarse grained Discrete(fine scale) Articulated Flexible Body Model – Coarse grained Efficient Multibody Dynamics Algorithms Efficient Force Calculations Multi-time Step Integration Schemes Adaptive Resolution Control -Generalized Momentum Formulation Adaptive Resolution Change : discrete, rigid and flexible models Adaptive Domain Change: H and P type refinement Better Fidelity and Faster Simulations 1/10/2022 Rensselaer Computational Dynamics Laboratory 12

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Efficient Design Sensitivity Determination for Multibody Systems q Design optimization of multibody systems (MBS) is time-consuming and complex tasks. Goals Modeling Validation q Optimization techniques with fast convergence (e. g. , gradientbased) are often beneficial within this context. 1/10/2022 Rensselaer Computational Dynamics Laboratory Analysis Simulation 16

Sensitivity Analysis q Sensitivity analysis plays an important role in gradient-based optimization techniques and modern engineering applications. q Sensitivity analysis is also an asset to: q Assessment of design trend q Control algorithm developments q Determination of coupling strength in multidisciplinary design optimization (MDO) 1/10/2022 Rensselaer Computational Dynamics Laboratory 17

Methods Developed Here Offer Considerable Computational Savings • “Exact” Senstitivity Methods Developed here O(n+m) [Cost Linear in n & m] O(n 4) Scale Simulation Time (seconds) • Traditional “Exact” Sensitivity Methods O(n 4) [Cost Quartic in n] O(n) Scale 2000 O(n 4) Empirical Data Best Fit Quartic 0. 5 1600 O(n ) Empirical Data Best Fit Linear 0. 4 0. 3 1200 0. 2 800 0. 1 400 0 2 4 6 8 10 12 Number of Degrees of Freedom n Examples: Simple Automobile Model: n=24, Detailed M 1 Abrams: n=952, Space Station: n>2000 1/10/2022 Collections of MEMS Devices: n~10000 Detailed Nano-Structure: n~105 Future Needs: n>? ? ? Rensselaer Computational Dynamics Laboratory 18

Methods Developed Here Offer Considerable Computational Savings Outcomes: • Dynamic Simulation cost O(n+m) overall [Traditionally O(n 3+nm 2+m 3) ] • Design Sensitivity Analysis cost O(n+m) overall [Traditionally O(n +n m +m ) ] 4 2 2 3 Research Spawned out of this Work (Funding Agency) • Efficient molecular dynamic modeling ( NSF NIRT†, Sandia†) • Multi-scale, multi-physics composite material modeling (NSF†, Sandia†) • Efficient track and drive chain modeling (A. R. O. †, MDI‡) • Virtual prototyping (Ford‡) • Distributed modeling/control of heavily redundant MEMS systems (NYSCAT‡, Zyvex‡) • Advanced computing aerospace system modeling (NASA) † Proposal submitted or soon to be submitted ‡ Collaboration or funding already established 1/10/2022 Rensselaer Computational Dynamics Laboratory 19