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the points satisfying Snell’s law). So one of the most important things in our numerical implementation is to determine the area on which the integral will be implemented. For this purpose ¥ we define � � � � � ¡ £ ¥ � ¨ ¥ § ¨ ¥ � � ¥ the vector on each coarse grid point. Once the scalar � product of ¥ and the � normal vector of the interface is greater than the threshold the integral will be computed on the fine cells around the coarse grid point (figure 1b). Numerical example We only consider a