In this project, the smoothed boundary method (SBM) is applied to solve a partial differential equation (diffusion) with an adaptive mesh refinement (AMR) technique to increase the numerical accuracy of simulating the diffusion process in a batter electrode. Fick’s second law of Diffusion is reformulated to a SBM diffusion equation with Neumann boundary conditions considered. A domain parameter is acquired through diffusion smoothing the microscopic images of an electrode, which is used to describe the 3D complex microstructure of the electrode. This image-based domain parameter is incorporated into the SBM to simulate the diffusion within the complex geometries. Adaptive mesh refinement with bottom up quad-tree analysis is utilized to refine the grid system in the interface regions of the microstructure. With this AMR technique, the diffusion process can be more accurately simulated.