The Rensselaer Polytechnic Institute Computational Dynamics Laboratory

Who are We? Faculty Professor Kurt S. Anderson Graduate Students Rudranarayan Mukherjee Kishor Bhalerao Mohammad Poursina

• • Rudranarayan Rudranarayan Mukherjee Mukherjee , PhD Student Focus: Focus: Evaluation of parallel algorithms for Evaluation of parallel algorithms for applicability to protein folding and macro applicability to protein folding and macro molecular dynamics molecular dynamics • • Past Researchers Past Researchers – – Shanzhong Shanzhong Duan Duan , Ph.D. , Ph.D. – – YuHung YuHung Hsu, Ph.D. Hsu, Ph.D. – – Omer Omer Gundogdu Gundogdu , Ph.D. , Ph.D. – – Jason Jason Rosner Rosner , MS , MS – – Philip Philip Stephanou Stephanou , MS , MS

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

Note: n= Number of System Generalized Coordinates, m = Number of System Constraints

Multi-Scale Multibody Dynamics Hierarchic Multi-resolution Substructured Model Articulated Flexible Body Model – Coarse grained Discrete(fine scale) Articulated Rigid 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

Efficient Design Sensitivity Determination for Multibody Systems Design optimization of multibody systems (MBS) is time-consuming and complex tasks. Goals Modeling Analysis Validation Simulation Optimization techniques with fast convergence (e.g., gradient-based) are often beneficial within this context.

Sensitivity Analysis Sensitivity analysis plays an important role in gradient-based optimization techniques and modern engineering applications. Sensitivity analysis is also an asset to: Assessment of design trend Control algorithm developments Determination of coupling strength in multidisciplinary design optimization (MDO)

Methods Developed Here Offer Considerable Computational Savings Traditional “Exact” Sensitivity Methods O(n4) [Cost Quartic in n] “Exact” Senstitivity Methods Developed here O(n+m) [Cost Linear in n & m] 1600 800 400 1200 2000 O(n) Scale O(n4) Empirical Data O(n ) Empirical Data Best Fit Quartic Best Fit Linear 2 4 6 8 10 12 O(n4) Scale 0.1 0.2 0.3 0.4 0.5 Number of Degrees of Freedom n Simulation Time (seconds) Examples: Simple Automobile Model: n=24, Collections of MEMS Devices: n~10000 Detailed M1 Abrams: n=952, Detailed Nano-Structure: n~105 Space Station: n>2000 Future Needs: n>???

Methods Developed Here Offer Considerable Computational Savings Outcomes: Dynamic Simulation cost O(n+m) overall [Traditionally O(n3+nm2+m3) ] Design Sensitivity Analysis cost O(n+m) overall [Traditionally O(n4+n2m2+m3) ] 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