Joint Numerical Analysis/Applied Mathematics Seminar

Friday, February 23, 2007

Speaker: John Strain, University of California at Berkeley
Title: Semi-Lagrangian Contouring and Elliptic Systems with Complex Moving Interfaces
Time: 3:00-4:00 pm
Place: Blocker 627

Abstract

Models of physical phenomena such as crystal growth or blood flow generally involve complex moving interfaces, with velocities determined by interfacial geometry and material physics. Numerical methods for such models tend to be customized. As a consequence, they must be redesigned whenever the model changes.

We present a general computational algorithm for evolving complex interfaces which treats the velocity as a black box, thus avoiding model-dependent issues. The interface is implicitly updated via an explicit second-order semi-Lagrangian advection formula which converts moving interfaces to a contouring problem. Spatial and temporal resolutions are decoupled, permitting grid-free adaptive refinement of the interface geometry. A modular implementation computes highly accurate solutions to geometric moving interface problems involving merging, anisotropy, faceting, curvature, dynamic topology and nonlocal interactions.

For many physical models, the black-box interface velocity is determined by an elliptic system of partial differential equations. We present a fast new solver for the equivalent boundary integral equations, based on Fourier analysis and classical Ewald summation.

Last revised: 02/05/07 By: christov@math