Million-to-Billion Atom Simulation of Chemical Reactions: Embedded Divide-and-Conquer and Hierarchical Cellular Decomposition Frameworks for Scalable Scientific Computing

Simulating chemical reactions involving billions of atoms has been a dream of scientists, with broad societal impacts. This paper realizes the dream through novel simulation methods, algorithms, and parallel computing and visualization techniques. We have designed O(N) embedded divide-and-conquer (EDC) algorithms for 1) first principles-based parallel reactive force-field (P-ReaxFF) molecular dynamics (MD), and 2) density functional theory (DFT) on adaptive multigrids for quantum mechanical MD, based on a space-time multiresolution MD (MRMD) algorithm. To map these O(N) algorithms onto parallel computers, we have developed a hierarchical cellular decomposition (HCD) framework, including 1) wavelet-based computational-space decomposition for adaptive load balancing, and 2) octree-based probabilistic visibility culling for interactive visualization of billion-atom datasets. Preliminary tests on 1,920 Itanium2 processors of the NASA Columbia supercomputer have achieved unprecedented scales of reactive atomistic simulations: 0.56 billion-atom P-ReaxFF and 1.4 million-atom (0.12 trillion grid points) EDC-DFT simulations, in addition to 18.9 billion-atom MRMD simulation.