Computation of initial data, II
Thursday, June 27, 2002 - 10:05am - 10:35am
In this second of two talks on the computation of initial data, we will focus on the boundary value problem arising in the York conformal decomposition of the initial data. We examine in some detail the resulting coupled Hamiltonian and momentum constraints, focusing first on some fundamental issues such as well-posedness and approximation theory. We then review some of the numerical methods which have been used previously to solve the equations under various simplifying assumptions. Finally, we discuss the treatment of the general coupled nonlinear elliptic system using error-driven adaptive finite element discretization, Gummel decoupling methods, and Newton-multilevel iterative methods. We finish by outlining some of the open research questions, from the perspective of a mathematician and numerical analyst.