Simulation boundary boundry model for multi-mode, multi-frequency signals using the Higdon operator

Boundary conditions for multi-mode, multi-frequency signals in high power and broad band applications require special attention to the details of boundary matching. In earlier work, we have found that the Higdon [1] operator provides the basis for a multi-phase velocity absorbing boundary condition where the impinging wave may be of different frequencies and modes. Using a second order implementation, the model allows for injection of waves with extremely low reflection coefficient into the interior of both cold test and hot test simulation environments as previously reported by the authors [2]. The key outcome is the near perfect absorption of scattered (outgoing) waves. Additionally, the model is insensitive to the presence of particles exiting or entering through these simulation boundaries [3]. We have implemented this model in both Cartesian and cylindrical formulations [2]. Additionally, in previous work the authors have looked at the 3^rd order Higdon operator where the implementation begins to get very cumbersome once the differential operators are recast into Finite Difference Operator form. Givoli and Neta [4] have suggested a method of recasting the solution in terms of auxiliary functions of arbitrarily high order. We will report on our implementation of this method.