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Applied Math Seminar
Fast Semi-Lagrangian Computations with Complex Interfaces
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Modeling of technological processes, such as faceted crystal growth, often produces PDEs in which distinct spatial regions are dominated by distinct physical effects, and separated by complex moving interfaces. The solutions of the PDEs determine interfacial velocities, and satisfy boundary conditions which are coupled to interfacial geometry and dynamics. We present a computational strategy for evolving complex interfaces which treats the velocity as a black box. The interface is implicitly updated via an explicit second-order semi-Lagrangian advection formula, then extracted with a high-order adaptive geometric contouring code. Spatial and temporal resolutions are decoupled, permitting grid-free adaptive refinement of the interface geometry. A modular implementation couples to any local or nonlocal velocity. |