Petascale Brownian dynamics simulations of highly resolved polymer chains with hydrodynamic interactions using modern GPUs

Brownian dynamics simulations of fairly long, highly detailed polymer chains, at the resolution of a single Kuhn step, remains computationally prohibitive even on the modern processors. This is especially true when the beads on the chain experience hydrodynamic interactions (HI), which requires the usage of methods like Cholesky decomposition of large matrices at every timestep. In this study, we perform Petascale BD simulations, with HI, of fairly long and highly resolved polymer chains on modern GPUs. Our results clearly highlight the inadequacies of the typical models that use beads connected by springs. In this manuscript, firstly, we present the details of a highly scalable, parallel hybrid code implemented on a GPU for BD simulations of chains resolved to a single Kuhn step. In this hybrid code using CUDA and MPI, we have incorporated HI using the Cholesky decomposition method. Next, we validate the GPU implementation extensively with theoretical expectations for polymer chains at equilibrium and in flow with results in the absence of HI. Further, our results in flow with HI show significantly different temporal variations of stretch, in both startup extensional and shear flows, relative to the conventional bead-spring models. In all cases investigated, the ensemble averaged chain stretch is much lower than bead-spring predictions. Also, quite remarkably, our GPU implementation shows a scaling of $\sim$$N^{1.2}$ and $\sim$$N^{2.2}$ of the computational times for shorter and longer chains in the most modern available GPU, respectively, which is significantly lower than the theoretically expected $\sim$$N^{3}$. We expect our methods and results to pave the way for further analysis of polymer physics in flow fields, with long and highly detailed chain models.