Parallelizable multibody algorithms for efficient multi-resolution modeling and simulation of dynamic systems

The objective of this research is to extend the current capabilities of the divide-and-conquer based suite of multibody dynamics algorithms, and to develop new methods to achieve superior computational efficiency in the dynamic simulations of complex systems. The target application area is the efficient and adaptive coarse-grain modeling and simulations of large biopolymeric systems. Typically, the size these molecules ranges from a few hundred atoms to millions of atoms, whereas their dynamics may involve temporal magnitudes ranging from sub-femtosecond to beyond millisecond. As such, advance simulation methods, that attempt to reduce the computational burden offered by these extremely important biological systems, can be of great importance. The methods that are developed in this research are general in nature and easily lend themselves to more traditional areas involving multibody systems. Therefore, important applications of the current research work are also found in robotics, vehicle dynamics, and real time simulations of articulated bodies, among others. The research work presented in this dissertation has its foundation in the highly parallelizable suite of divide-and-conquer algorithms (DCA) for multibody systems. These methods provide a mathematical formulation for the efficient simulations of complex biopolymeric systems. To this extent, the present work focuses on extending the current capabilities of the DCA-based framework, thereby permitting adaptive modeling and simulation of the dynamic behavior of complex multibody systems, to a level greatly beyond what is currently possible (in terms of the size of the system, fidelity, and simulation time). This dissertation addresses this issue at three different levels. First, new algorithms are introduced to accompany previously proposed DCA-based multibody dynamics methods. Additionally, new techniques are developed that permits on-the-fly transitions between models with varying level of fidelity and/or changes in model types. Finally, adaptive simulation methods are developed, such that a high level of accuracy may be achieved in the computer simulations of multibody systems at minimum computational cost. This dissertation presents a constraint stabilization technique for the orthogonal complement-based divide-and-conquer algorithm (ODCA). The constraint stabilization allows long time simulations of kinematically constrained systems by controlling the growth in the constraint satisfaction error. Mathematical derivation of the new method is presented and its validity is demonstrated using several numerical examples. A new algorithm is presented for modeling multi-flexible-body systems in a floating frame of reference formulation. The new method utilizes interpolating splines to model the deformation field of the flexible bodies, and has several advantages over the previous capability in the DCA for modeling articulated deformable bodies. Necessary mathematics is developed and the usefulness of the splines-based DCA is established using numerical test cases. This research presents a novel method for modeling large deformations within the DCA framework. The new algorithm utilizes existing finite element formations to model highly elastic systems undergoing large rotations. The present method is tested using the absolute nodal coordinate formulation and it achieves linear and logarithmic complexity when implemented in serial and parallel, respectively. Necessary equations for the new method are derived and several numerical examples are also presented. On-the-fly transitions between models with different resolutions is the key to adaptive multibody simulations. This research presents new methods for achieving these model changes in articulated multi-flexible-body systems with focus on coarse-grained molecular dynamics. Present algorithm allows transition from a coarse scale model to a fine scale model and vice versa. The generalized momentum of the system remains conserved during these transitions and the issue of discontinuous changes in system energy is also discussed. Finally, new techniques for performing adaptive simulations in multibody systems are presented. The present methods utilize existing and newly developed capabilities in the DCA to achieve simplified yet accurate models, such that the computational efficiency associated with their simulations can be maximized. These adaptive simulations may automatically be guided by internal metrics indicators or by other user defined criterion. Different aspects of the adaptive simulations are tested using several numerical examples.