1. The Rensselaer Polytechnic Institute Computational Dynamics Laboratory

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

5. • • 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

7. 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

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

12. 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

16. 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.

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. 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> Future Needs: n>???

19. 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