Fast Computational Modules for Moving Interfaces

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

The investigators will develop, analyze, implement and distribute robust, efficient and accurate new algorithms for evolving complex interfaces determined by general partial differential systems. Two interacting modular components are combined: general interface motion under a given velocity, and the problem-specific velocity of a given moving interface. The first component involves semi-Lagrangian contouring, with fast stable tools for geometric operations such as contouring, distancing and intersection. Efficient algorithms convert between explicit and implicit interface representations with fast computational geometry, robust global topology resolution, and high-order Bezier representations, to track complex surfaces evolving under arbitrary dynamics and topology. The second component requires high-accuracy solution of partial differential systems for material fields, stresses and concentrations, which determine the velocity of the interface. Fast accurate solvers for algebraically complete first-order formulations split Green functions into singular and global terms, and achieve optimal efficiency for elliptic/parabolic systems with complex interfaces. The interface motion and velocity evaluation components connect through new implicit time-stepping schemes which handle sensitive interface velocities stably. The Frechet derivatives incurred in the solution of implicit schemes are systematically decomposed into universal components, and computed by efficiently reusable computational modules. Mathematical models of complex evolving material interfaces dominate technological processes ranging from semiconductor production to surgery planning, from computer animation to computer-controlled machine tooling. Efficient general computational techniques are crucial in designing better models. The investigators are developing efficient new modular computational tools for simulating technological processes in robust user-friendly ways. This highly interdisciplinary enterprise combines mathematics and computer science to benefit scientific endeavors ranging from cartography to crystallography. The research objectives intertwine with an interdisciplinary educational program, training future scientists and engineers through web-enabled courses, math/science/engineering seminars and individual student research mentoring.