Many problems of scientific, engineering, industrial, medical, or safety interest are cast as “deforming boundary problems”. A partial list of example problems are the prediction of the evolution of the burnt regions of a forest fire, shape recognition and pattern matching, atomization and spray in jet or diesel engines, aircraft wing icing, shock waves from aircraft, shape optimization for withstanding loads, design of microswimmers (targeted drug delivery), crystal growth, breaking waves, tumor growth, crack formation and propagation, and radiation therapy. A numerical method can give insight to physical processes, or provide optimal solutions, that are not as easily obtainable through experiments or other manual means of information gathering. There are a myriad of techniques for simulating deforming boundary problems. In this presentation, an overview of the methods used (such as Weighted Essentially Non-Oscillatory, Level Set, Ghost Fluid, shock fitting, Adaptive Mesh Refinement, to name just a few), and a road map for which method is best for which problem is given.

Mark Sussman was born in San Diego, California in 1966. He graduated from San Diego State University in 1986 (Bachelor's degree in Applied Mathematics, minor in physics and computer science), and University of California, Los Angeles in 1994 (PhD degree in mathematics, advisor S. Osher). Mark Sussman's employment history includes two years as a postdoc at Lawrence Livermore/Berkeley National Laboratory, three years as a visiting research assistant professor at University of California Davis, and 16 years at Florida State University (now a professor in the Mathematics department). His research specializes in numerical methods for deforming boundary problems with applications to multiphase flow. Mark Sussman has authored/co-authored many articles in refereed archival journals, served as a referee for articles submitted to archival journals in the fields of mathematics, engineering, biology, chemistry, and computer science, and has served on many proposal review panels.