Noniterative Domain Decomposition for Second Order Hyperbolic Problems

The solutions of damped second order hyperbolic problems can have smooth components which decay slowly and rough components which decay quickly. If the behavior of the solution is of interest on the time scale of the slowly-decaying modes, then implicit time stepping methods may be more efficient than explicit methods. We formulate and analyze a Galerkin method for approximating the solutions of second order hyperbolic problems. This method involves domain decomposition in its formulation rather than as a means of solving the elliptic problems that result at each time step when a usual implicit method is used