James Sethian

Developing computational tools that enable discovery of new materials for energy-related applications is a challenge. Crystalline porous materials are a promising class of materials that can be used for oil refinement, hydrogen or methane storage as well as carbon dioxide capture. Selecting optimal materials for these important applications requires analysis and screening of millions of potential candidates. Recently, we proposed an automatic approach based on the Fast Marching Method (FMM) for performing analysis of void space inside materials, a critical step preceding expensive molecular dynamics simulations. This breakthrough enables unsupervised, high-throughput characterization of large material databases. The algorithm has three steps: (1) calculation of the cost-grid which represents the structure and encodes the occupiable positions within the void space; (2) using FMM to segment out patches of the void space in the grid of (1), and find how they are connected to form either periodic channels or inaccessible pockets; and (3) generating blocking spheres that encapsulate the discovered inaccessible pockets and are used in proceeding molecular simulations. In this work, we expand upon our original approach through (A) replacement of the FMM-based approach with a more computationally efficient flood fill algorithm; and (B) parallelization of all steps in the algorithm, including a GPU implementation of the most computationally expensive step, the cost-grid generation. We report the acceleration achievable in each step and in the complete application, and discuss the implications for high-throughput material screening.

We introduce a numerical framework, the Voronoi Implicit Interface Method for tracking multiple interacting and evolving regions (phases) whose motion is determined by complex physics (fluids, mechanics, elasticity, etc.), intricate jump conditions, internal constraints, and boundary conditions. The method works in two and three dimensions, handles tens of thousands of interfaces and separate phases, and easily and automatically handles multiple junctions, triple points, and quadruple points in two dimensions, as well as triple lines, etc., in higher dimensions. Topological changes occur naturally, with no surgery required. The method is first-order accurate at junction points/lines, and of arbitrarily high-order accuracy away from such degeneracies. The method uses a single function to describe all phases simultaneously, represented on a fixed Eulerian mesh. We test the method’s accuracy through convergence tests, and demonstrate its applications to geometric flows, accurate prediction of von Neumann’s law for multiphase curvature flow, and robustness under complex fluid flow with surface tension and large shearing forces.