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A new method of solution to the local spin density approximation to the electronic Schr{o}dinger equation is presented. The method is based on an efficient, parallel, adaptive multigrid eigenvalue solver. It is shown that adaptivity is both necessary and sufficient to accurately solve the eigenvalue problem near the singularities at the atomic centers. While preliminary, these results suggest that direct real space methods may provide a much needed method for efficiently computing the forces in complex materials.
In this paper, we propose a parallel and scalable approach for geodesic distance computation on triangle meshes. Our key observation is that the recovery of geodesic distance with the heat method from [Crane et al. 2013] can be reformulated as optimi
Material scientists are increasingly adopting the use of machine learning (ML) for making potentially important decisions, such as, discovery, development, optimization, synthesis and characterization of materials. However, despite MLs impressive per
Particle-in-cell methods couple mesh-based methods for the solution of continuum mechanics problems, with the ability to advect and evolve particles. They have a long history and many applications in scientific computing. However, they have most ofte
Microstructures of a material form the bridge linking processing conditions - which can be controlled, to the material property - which is the primary interest in engineering applications. Thus a critical task in material design is establishing the p
Deep learning recommendation models (DLRMs) are used across many business-critical services at Facebook and are the single largest AI application in terms of infrastructure demand in its data-centers. In this paper we discuss the SW/HW co-designed so