The Rensselaer Polytechnic Institute Computational Dynamics Laboratory

1. The Rensselaer Polytechnic Institute Computational Dynamics Laboratory

2. Who are We? • FacultyProfessor Kurt S. Anderson • Graduate StudentsRudranarayan MukherjeeKishor BhaleraoMohammad Poursina

5. • • Rudranarayan Rudranarayan Mukherjee Mukherjee , PhD Student , 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

7. What Do We Do? • A Unified ApproachBridging 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

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

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

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

17. 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)

18. O(n4) Scale O(n) Scale O(n4) Empirical Data Best Fit Quartic 0.5 2000 O(n) Empirical Data 0.4 1600 Best Fit Linear 0.3 Simulation Time (seconds) 1200 0.2 800 0.1 400 10 12 0 6 8 2 4 Number of Degrees of Freedom n Methods Developed Here OfferConsiderable Computational Savings • Traditional “Exact” Sensitivity Methods O(n4) [Cost Quartic in n] • “Exact” Senstitivity Methods Developed hereO(n+m) [Cost Linear in n & m] 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>???

19. Methods Developed Here OfferConsiderable 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