This work presents a method for recursively assembling tensor-like quantities that parameterize the charge distribution of rigid bodies, which result from model reduction of biopolymeric systems using an articulated multibody approach. This is done with the goal of reducing the computational cost associated with the pairwise force determination encountered in molecular dynamics simulations. To achieve a linear computational cost complexity of the force determination, with respect to the number of bodies in the system (N), a recursive assembly and disassembly (evaluation) sweep is proposed. This work proposes assembling these tensor quantities (pseudo-inertia tensors), which are associated with the body’s charge distribution, with a method that uses the standard parallel axis theorem to shift these tensors to a common point so they may be summed.
This work presents a preliminary numerical example that examines the accuracy of the force and moment computation using a pseudo-inertia tensor resulting after one level of recursive assembly. The Coulomb force and associated moment on a target body due to the assembled body is computed. The test problem approximates a system that is highly negatively or positively charged. The orientation of the bodies that are assembled is varied, along with the distance between the assembly and the target body. The preliminary results presented herein suggest that this is a viable method of efficiently representing the charge distribution of an assembly. The numerical example presented determines the Coulomb force and the associated moment, as a function of distance and the pseudo-inertia tensor. However, the approximation can be used for any force that is of the form 1/rs, where s is any power.
