TY - JOUR
T1 - Model transitions and optimization problem in multi-flexible-body systems
T2 - Application to modeling molecular systems
AU - Khan, I. M.
AU - Poursina, M.
AU - Anderson, K. S.
N1 - Funding Information:
The authors would like to acknowledge the financial support of the Division of Civil, Mechanical & Manufacturing Innovation of the National Science Foundation (grants # 0757936 and 1161872 ).
PY - 2013/7
Y1 - 2013/7
N2 - This paper presents an efficient algorithm for the simulation of multi-flexible-body systems undergoing discontinuous changes in model definition. The equations governing the dynamics of the transitions from a higher to a lower fidelity model and vice versa are formulated through imposing/removing certain constraints on/from the system model. The issue of the non-uniqueness of the results associated with the transition from a lower to a higher fidelity model may be handled by solving an optimization problem. This optimization problem is subjected to the satisfaction of the constraint imposed by the generalized impulse-momentum equations. The divide-and-conquer algorithm (DCA) is applied to formulate the jumps in the system states resulting from the model transition. The DCA formulation in its basic form is both time and processor optimal and results in linear and logarithmic complexity when implemented in serial and parallel with O(n) processors, respectively. As such, its application can reduce the effective computational cost of formulating and solving the optimization problem in the transitions to the finer models. The principal aspects of the mathematics for the algorithm implementation is developed and numerical examples are provided to validate the method.
AB - This paper presents an efficient algorithm for the simulation of multi-flexible-body systems undergoing discontinuous changes in model definition. The equations governing the dynamics of the transitions from a higher to a lower fidelity model and vice versa are formulated through imposing/removing certain constraints on/from the system model. The issue of the non-uniqueness of the results associated with the transition from a lower to a higher fidelity model may be handled by solving an optimization problem. This optimization problem is subjected to the satisfaction of the constraint imposed by the generalized impulse-momentum equations. The divide-and-conquer algorithm (DCA) is applied to formulate the jumps in the system states resulting from the model transition. The DCA formulation in its basic form is both time and processor optimal and results in linear and logarithmic complexity when implemented in serial and parallel with O(n) processors, respectively. As such, its application can reduce the effective computational cost of formulating and solving the optimization problem in the transitions to the finer models. The principal aspects of the mathematics for the algorithm implementation is developed and numerical examples are provided to validate the method.
KW - Adaptive simulations
KW - Divide-and-conquer algorithm
KW - Model transitions
KW - Molecular dynamics
KW - Multi-flexible-body dynamics
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U2 - 10.1016/j.cpc.2013.02.025
DO - 10.1016/j.cpc.2013.02.025
M3 - Article
AN - SCOPUS:84875861228
SN - 0010-4655
VL - 184
SP - 1717
EP - 1728
JO - Computer Physics Communications
JF - Computer Physics Communications
IS - 7
ER -