HYPERSURFACES MOVING WITH CURVATURE-DEPENDENT SPEED: HAMILTON-JACOBI EQUATIONS, CONSERVATION LAWS AND NUMERICAL ALGORITHMS

摘要: In many physical problems, interfaces move with a speed that depends on the local curvature. Some common examples are flame propagation, crystal growth, and oil-water boundaries. We model front as closed, non-intersecting, initial hypersurface flowing along its gradient field Because explicit solutions seldom exist, numerical approximations often used. The goal of this paper is to show algorithms based direct parameterizations moving face considerable difficulties. This because such adhere properties solution, rather than global structure. Conversely, motion can be captured by imbedding surface in higher-dimensi onal function. setting, equations solved using techniques borrowed from hyperbolic conservation laws. use these schemes follow variety propagation illustrating corner formation, breaking merging.