Conformal mapping of a doubly-connected polygonal domain onto an annulus

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Currently, I have a domain D that is bounded by two polygons $C_1$ and $C_2$ (with $C_2$ completely 'inside' $C_1$). Now I want to map this domain onto $D'$ with the outer circle $C_1'$ (with unit radius) and $C_2'$ (with radius smaller than 1). There exists an inverse Schwarz-Christoffel mapping that maps a polygon onto the unit circle, but that is only applicable for a simply connected domain. How do I find a transformation that maps $D$ onto $D'$?