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The solution of a propagation problem is subject to initial conditions specified at a particular value of the timelike coordinate and boundary conditions specified at each point on the spacelike boundary. The domain of interest D(x, t) is open in the direction of the timelike coordinate. Figure IlIA illustrates the open solution domain D(x, t) and its boundary B which is composed of the initial time boundary and the two physical boundaries. Propagation problems are initial-value problems, which are solved by marching methods.