[SY-F2] Symposium F-2

[SY-F2] New algorithms for simulating grain boundary motion

Invited

^○Selim Esedoglu (University of Michigan, United States of America)

I will describe the latest developments in a class of algorithms known as threshold dynamics for simulating the motion of interfaces under curvature and related flows, as appears in many models of grain boundary motion. These are remarkably elegant algorithms that generate the desired evolution, along with all the correct boundary conditions along junctions, by alternating two very simple and efficient procedures: Convolution with a kernel and thresholding. They allow arbitrarily large time steps, and handle topological changes automatically. The most recent versions allow specifying N-choose-2 anisotropic (normal dependent) surface tensions and anisotropic (normal dependent) mobilities for a network of N grains. We will describe simple and explicit formulas that tell us how to bake in the desired set of mobility and surface tension functions into the algorithm.