A new approach to the time-domain analysis of scattering problems is presented. In this approach, the Kirchhoff-type formulas are interpreted as explicit Dirichlet boundary conditions that can be posed on any artificial boundary that encloses a scattering object. These boundary conditions are updated as computations proceed. The physical foundation for this approach is the retardation phenomena. First- and second-order formulations of this approach are discussed and some preliminary numerical results are reported.
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