Recent experimental STM images [1-4] of the surfaces of Cu(111) and Au(111) have demonstrated the direct measurement of the local density of electronic states (LDOS) for the system of a two-dimensional electron gas (2DEG) in the vicinity of geometrically arranged scattering centers (Fe adatoms). We report on our numerical method and calculations of the LDOS for these "quantum corral" structures. The numerical technique implements non-reflecting boundary conditions on an artificial boundary enclosing the scattering domain and is compatible with standard finite element methods. Excellent agreement is achieved in a comparison of both the calculated energy spectra of the LDOS and the spatial variation of the LDOS with the recently reported experimental STM data [3,4]. Contrary to the results of the multiple scattering theory reported by Heller et al. [4], our results demonstrate that a completely coherent elastic scattering model in an open boundary system is sufficient to explain the reported experiments with comparable agreement.
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