A. Globus,C. Levit,and T. Lasinski RNR Technical Report RNR-91-017
April,1991
We describe a software system,TOPO,that numerically analyzes and graphically displays topological aspects of a three dimensional vector field v to produce a single,relatively simple picture that characterizes v. The topology of v that we consider consists of its critical points (where v+0) their invariant manifolds, and the integral curves connecting these invariant manifolds.Many of the interesting features of v are associated with its critical point as approximated by the Taylor expansion.The coefficients of the first non-zero term of the Taylor expansion around a crucial point are the 3x3 matrix v. Critical points are classified by examining v's eigenvalues. The eigenvectors of v span the invariant manifolds of the linearized field around a critical point.Curves integrated from initial points on the eigenvectors a small distance from a critical point connect with other critical points (or the boundary) to complete the topology. In addition,one class of critical surfaces important in computational fluid dynamics is analysed.