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In this paper we propose a multilevel non-linear programming based 3D placement approach that minimizes a weighted sum of total wirelength and TS via number subject to area density constraints. This approach relaxes the discrete layer assignments so that they are continuous in the z-direction and the problem can be solved by an analytical global placer. A key idea is to do the overlap removal and device layer assignment simultaneously by adding a density penalty function for both area & TS via density constraints. Experimental results show that this analytical placer in a multilevel framework is effective to achieve trade-offs between wirelength and TS via number. Compared to the recently published transformation-based 3D placement method, we are able to achieve on average 12% shorter wirelength and 29% fewer TS via compared to their cases with best wirelength; we are also able to achieve on average 20% shorter wirelength and 50% fewer TS via number compared to their cases with best TS via numbers.