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Wave propagators are introduced for transient wave propagation in a general one-dimensional medium. The definition of wave propagators is based upon a wave splitting technique. Several properties for the propagators are given and the relations between the method of propagators and the invariant imbedding method and the Green function approach are discussed.
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The traditional multiscale approach couples two models operating at different scales. An alternative modelling strategy, called peridynamics originally developed by [1], is to continualize the molecular dynamic models, thus replacing inhomogeneities present on smaller length scales by an enhanced continuum description on larger length scales resulting in a nonlocal reformulation of continuum mecha