Computational Physics Meets Computational Geometry

Front Tracking is a methodology which uses computational geometry to provide numerical solutions of enhanced quality for problems of computational physics. It is particularly applicable to the computation of solutions with important jump discontinuities, or fronts. Fronts are represented as lower dimensional data structures, which in the spirit of non-manifold geometries used in CAD systems, support surfaces, curves (at surface intersections) and nodes (at common intersection points of three surfaces). These are expressed in the front tracking algorithm as a simplicial complex: data structures representing non intersecting smooth objects of given dimension, and boundary and coboundary operators to link them to lower and higher dimensional smooth objects. In the solution to problems of computational physics, these fronts evolve and can change their topology, forcing the need for fast retriangulation, intersection detection, and intersection removal routines. The methodology has been app..