Related numerical and analytical ideas including high resolution numerical methods, convolution generated motion, threshold dynamics, dynamic surface extension, cellular automata, stochastic partial differential equations and harmonic maps, some of which are quite novel, some of which are classical, are relevant to Geometrically Based Motions. Other applications continue to arise. The goal of the program is to foster working relationships among researchers studying mathematical and numerical techniques and people doing real world applications. Mathematicians, statisticians, computer scientists, and biologists from academia and from industry are all invited to attend. An Overview and Some Recent Results , Stanley Osher and Ronald P. Fedkiw.
Eikonal equations describe the evolution of the singular support of solutions to wave equations.
Computing these wave fronts is usually done via ray tracing methods. Recently, innovative numerical and semianalytic techniques have been developed using alternative partial differential equation and geometrically based techniques. Efficient numerical methods for these problems, and for solving the associated transport equations will be discussed. This workshop will bring together mathematicians and computer scientists with scientists from the applied fields. Many problems in material sciences involve the motion of geometric objects such as interfaces or filaments.