The image shows a portion of a slice across an unstructured adaptive tetrahedral mesh which triangulates the region complementary to two spheres in three dimensional space. The colored triangles are the intersections of the tetrahedra with the slicing plane. They have been shrunk slightly for better visibility. The edges of the mesh which intersect the boundary are displayed in black. These lie on the spheres and also on a much larger containing sphere which is used as an artificial boundary. The colors indicate the values of the finite element solution to a nonlinear elliptic boundary value problem computed on this mesh.

The problem under consideration is the computation of compatible initial data for the Einstein field equations to simulate the collision of two black holes. The quantity computed is the conformal factor for a conformally flat Lorenzian metric satisfying the constraint equations arising from the Einstein equations. The program was written by Arup Mukherjee and is described, together with this and other computations, in his thesis.

Last modified April 19, 1999 by Douglas N. Arnold,