A Multiscale Atomistic Method for Long-Range Electrical Interactions Accounting for Finite-Temperature Thermal Fluctuations
Abstract
Major Goals: This project will develop multiscale atomistic methods for complex functional and electronic materials. The central challenge from the perspective of computational mathematics is that in ionic / polarizable / dielectric solids broadly, the long-range interaction between atoms plays an critical role. Existing multiscale atomistic methods cannot efficiently deal with this challenge; they are suitable only when atomic interactions are short-range with nearby neighbors, e.g. as in metals. However, the Coulombic interactions are long-range (decay with inverse first power of distance), and interactions between every pair of charges in the system are important; naive truncations can cause large errors. Further, due to the strongly-coupled multiscale nature of the problem, approaches that assume complete separation-of-scales are not applicable. This proposal will build on prior work by the PI and his collaborators that developed a fast method to coarse-grain electrical interactions in crystals. The technical strategy coarse-grains the electrical interactions by exploiting the fact that the crystal was close-to-periodic in regions away from the defect. The use of adaptive discretizations enables the design of a numerical algorithm that is many orders faster than the available methods while maintaining a desired accuracy. This approach, however, is confined to zero-temperature settings; while it provides an essential first step, realistic scientific challenges require the accounting of temperature. This leads to a computational mathematics challenge of accounting for interactions in systems where the charges fluctuate about their mean positions. Our technical strategy will build on probabilistic methods that are used for short-range interactions and adapt the electrostatics calculations to these settings. Another challenge in electrical interactions is that problems are generically posed on an unbounded domain with complicated boundary conditions; e.g., electrodes are surfaces of constant potential (Dirichlet boundary conditions) on the interior of the domain. We will use boundary elements and Dirichlet-to-Neumann maps to truncate the computational domain without introducing spurious artifacts.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Oct 11, 2018
- Source ID
- W911NF1710084
Entities
People
- Kaushik Dayal
Organizations
- Army Contracting Command
- Massachusetts Institute of Technology
- United States Army