Algorithms for Multiple Phases

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

This project will develop rigorously understood, highly efficient and accurate computational tools (algorithms and their software implementation, based on a solid theoretical foundation) for simulating the motion of networks of surfaces under geometric motions such as motion by weighted mean curvature and motion by surface diffusion. The approach is based on a new, variational formulation of threshold dynamics (also known as diffusion generated motion) of Merriman, Bence, and Osher that makes it possible to correctly extend the original algorithm to e.g. weighted mean curvature flow of multiple phases with unequal and anisotropic surface tensions. The geometric motions that will be studied in this project play a central role in materials science, where they describe the microstructural evolution of polycrystalline materials under common industrial processes such as annealing (heat treatment). Polycrystalline materials are very common: most metals and ceramics belong to this category. They are composed of tiny single-crystal pieces, known as grains, that are joined together along their faces. The physical properties of these materials, such as conductivity and yield strength, depend intimately on their microstructure (the shapes and sizes of the grains that make up the material). This project will advance our ability to simulate how the microstructure of these materials change, which is important for computational design of materials, where computer simulations rather than costly experiments would identify the most favorable processing parameters for achieving desired characteristics.