The reliability of LDMOSFET as well as FinFET devices has been gaining much interest in the development of various space electronic systems. There are high requirements for nonlinear computation and efficient simulation of radiation-multiphysics effects in these devices, especially in large-scale 3D scenarios, which pose significant challenges. To address these issues, we propose a hybrid numerical method for massively parallel simulation of nonlinear drift-diffusion transport processes in semiconductor devices. The control volume finite element method (CV-FEM) is employed to solve the Poisson, current continuity, and heat conduction equations, which shows strong numerical stability on unstructured meshes compared with the commercial COMSOL Multiphysics software. Further, our self-developed solver is employed to explore the total ionizing dose (TID)-electrothermal synergistic effects in step-doped LDMOSFETs (SD-LDMOSFETs), high-K dielectric SD-LDMOSFETs (HKSD-LDMOSFETs), and multi-fin FinFETs (M-FinFETs). We also implement a combined domain decomposition and J parallel Adaptive Unstructured Mesh applications Infrastructure scheme for parallel computation, where the scalability of our parallel algorithm is examined. It it believed that this study can offer some new insights into the behavior of these devices under radiation and electrothermal coupling, advancing efficient numerical methods to simulate diverse radiation-electrothermal synergistic effects.