The scaled boundary finite element method (SBFEM) is a semi-analytical computational technique [1] for the solution of partial differential equations, combining the advantages of finite element discretization with analytical representation in the radial direction. By reducing the spatial dimension of the governing problem, SBFEM has proven effective for a wide range of elliptic and time dependent analyses in computational mechanics. This work presents a dual-grid strategy within the scaled boundary finite element method for the efficient solution of semilinear elliptic and time dependent partial differential equations. The proposed approach addresses nonlinear reaction diffusion type problems in which the solution is obtained using a Newton based iterative scheme. Similar dual-grid or two-level strategies have previously been explored in other numerical frameworks, such as the virtual element method (VEM) [2], to enhance nonlinear convergence and computational efficiency. In the dual-grid framework, the semilinear problem is first solved on a coarse grid until convergence. The resulting solution is then interpolated onto a refined grid and employed as the initial guess for the Newton iterations on the fine grid. This coarse to fine transfer significantly improves the quality of the initial iterate and reduces the number of Newton iterations required for convergence on the fine grid. Numerical results demonstrate that the proposed dual-grid SBFEM achieves accuracy comparable to conventional single-grid fine-mesh solutions while offering a notable reduction in overall computational time. The reduction in computational cost becomes more pronounced for nonlinear problems, where Newton convergence is highly sensitive to the choice of the initial guess. Owing to its simplicity, scalability, and efficiency, the proposed dual-grid framework provides a practical acceleration technique for semilinear analyses and offers potential for extension to more complex nonlinear and multiphysics problems in computational mechanics.