SCATTERING BY A BOUNDED INHOMOGENEITY
This chapter continues the approximation of the field scattered by a bounded object. In this case, a penetrable scatterer (i.e., not a perfect conductor) is considered and the analysis of the previous chapter is extended by considering the effect of discretizing the Calderon map. A Lagrange multiplier on the artificial boundary is used to couple the field exterior to the artificial sphere to the finite element method inside the sphere. This allows a decoupling of the exterior and interior problems. The discrete problem is shown to be well posed, and the convergence of the resulting finite element and Lagrange multiplier method is verified using the collective compactness approach first used in Chapter 7.
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