As computational bounds are pushed, application codes are expected to solve more complex physics. One way the community is attempting to achieve this is to couple multiple "single application" codes together to address the more complex simulation. This leads to a variety of design difficulties based on how the coupling is implemented. Both the type of coupling and required solution techniques can have a significant impact on the performance and reliability of the resulting coupled code. We will present an algorithm that robustly solves coupled circuit simulation between a low fidelity lumped parameter circuit simulator and a high fidelity PDE simulation for the drift diffusion equations (similar to convection/diffusion/reaction PDEs). Each code is highly nonlinear and requires specific Globalized Newton-based techniques to robustly solve equations to the required accuracy. The application globalizations turn out to be incompatible with each other. In order to achieve tight coupling and robust performance, a nonlinear elimination technique has been implemented that allows each code to use its own globalization technique. Results will be shown for large-scale parallel circuits using the Xyce circuit simulator and Charon PDE solver developed by Sandia National Labs.