Fast Far-Field Potential Evaluation in Multibody-Based Simulations of Biopolymers

A novel algorithm to approximate the long-range potential field in multiscale simulations of biopolymers is presented. These models contain various domains including single particles, as well as regions with coarse-grained clusters in which high frequency modes of motion are suppressed. Herein, coarse-grained regions are formed via treating groups of atoms as rigid and/or flexible bodies/clusters connected together via kinematic joints, and as such, multibody dynamic techniques are used to form and solve the equations of motion. In such simulations with n particles, the evaluation of the potential field with computational complexity of O(n2), if not performed wisely, may become a bottleneck. This paper presents the approximation of the potential field due to the interaction between a charged particle and a body containing charged particles. This approximation is expressed in terms of physical and geometrical properties of the bodies such as the entire charge of the cluster and a pseudo-inertia tensor. Further, a divide-and-conquer scheme is introduced to implement the presented far-field potential evaluations. In this scheme adjacent charged bodies are combined together to form new bodies. The mathematical framework to create these new assemblies is presented. Then the potential of the resulting bodies on the charged particles which are far from them are recursively calculated.

Multi-Flexible-Body Simulations Using Interpolating Splines in a Divide-and-Conquer Scheme

A new method for modeling multi-flexible-body systems is presented that incorporates interpolating splines in a divide-and-conquer scheme. This algorithm uses the floating frame of reference formulation and piece-wise interpolation spline functions to construct and solve the non-linear equations of motion of the multi-flexible-body systems undergoing large rotations and translations. We compare the new algorithm with the flexible divide-and-conquer algorithm (FDCA) that uses the assumed modes method and may resort to sub-structuring in many cases [1]. We demonstrate, through numerical examples, that in such cases the interpolating spline-based approach is comparable in accuracy and superior in efficiency to the FDCA. The algorithm retains the theoretical logarithmic complexity inherent to the divide-and-conquer algorithm when implemented in parallel.

Operational Space Impulse Momentum Algorithm for Flexible Multibody Systems With Generalized Topologies

This paper presents a new methodology for modeling discontinuous dynamics of flexible and rigid multibody systems based on the impulse momentum formulation. The new methodology is based on the seminal idea of the divide and conquer scheme for modeling the forward dynamics of rigid multibody systems. While a similar impulse momentum approach has been demonstrated for multibody systems in tree topologies, this paper presents the generalization of the approach to systems in generalized topologies including many coupled kinematically closed loops. The approach utilizes a hierarchic assembly-disassembly process by traversing the system topology in a binary tree map to solve for the jumps in the system generalized speeds and the constraint impulsive loads in linear and logarithmic cost in serial and parallel implementations, respectively. The coupling between the unilateral and bilateral constraints is handled efficiently through the use of kinematic joint definitions. The generalized impulse momenta equations of flexible bodies are derived using a projection method.