Efficient Algorithms for Interface Motion and Wave Propagation

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

The proposed work will develop mathematical and numerical techniques to make computer algorithms more efficient in several key manufacturing and engineering processes. The work will focus on (i) semiconductor manufacturing to create faster and more reliable computer chips; (ii) seismic imaging to efficiently and accurately locate petroleum reserves; (iii) fluid jetting devices in the construction of computer display devices, bio-engineering of tissue scaffolding, and micro-jetting tools for printing circuit boards; (iv) injection molding and part manufacturing, and (v) logistical transport to determine optimal routing of goods and robotic motion. These topics are linked through the requirement to efficiently, accurately, and robustly track the motion of complex interfaces. Moving interface problems, which describe how boundaries move under intricate physics, are at the core of a host of practical and critical engineering and manufacturing problems. As examples, semiconductors are built through multiple processes of shaping, depositing, and etching the interfaces between chemicals. Seismic imaging in petroleum analysis requires fast solutions of propagating waves through the earth. Fluid jetting devices, which appear across a range of scales from desktop inkjet printers down to automatic bioassay testing, require careful attention to the moving fluid interface problems between air, fluids (such as ink), and solid walls. Injection molding requires carefully tracking the evolving boundaries between liquid, molten, and solid plastic as they fill a pre-formed mold. Logistical transport and robotics require tracking optimal control interfaces to determine first arrivals. The proposed work will be two-fold. First, previous NSF support has allowed us to develop many of the current state-of-the-art numerical techniques for tracking moving interfaces, including level set methods, fast marching methods, ordered upwind methods, and escape arrival methods; this work will continue through a focus on more efficient versions and extensions to more complex physics. Second, we will concentrate on prototype codes in each of the above-listed areas, in collaboration with industrial scientists, with the goal of creating practical engineering algorithms and simulations.