| Triangulations are playing an increasing role in applied mathematics and computational physics. Since they are much more complicated to code than rectangular grids, irregular triangulations become worthwhile for data representation only when the numerical problem is sufficiently large.; Many physical problems can be reduced to the evolution of two dimensional surfaces. Being highly nonuniform and sometimes fractal, these surfaces require special techniques for their description. Among the most important properties needed are locality and flexibility of the numerical model. To date, the Dynamical Triangulations (DT) have been the only technique capable of meeting such requirements.; The objective of this thesis has been to develop the applications of DT methods to various physical problems. I describe here the DT approach to smooth surface reconstruction from scattered data points, to three dimensional vortex sheets evolution and to quantum gravity. In all three cases, the DT has proven to be either the most efficient or the only possible way to deal with the problem. |
