Presented here is a new model of the solid-Earth response to tides and mass changes in ice sheets, oceans, and groundwater, in of terms of gravity change and bedrock motion. The model is capable simulating mantle deformation including elasticity, transient and steady-state viscous flow. We detail our approach to numerical optimization, and report the accuracy of results with respect to community benchmarks. The resulting coupled system features kilometer-scale resolution and fast computation.