The complexity of microstructures (and/or moving boundaries) makes conventional continuum-level simulations that involve complex microstructures very challenging. In this talk, we will present the Extended Smoothed Boundary Method (SBM), which uses a phase-field-like domain parameter to define the bulk domain where the partial differential equations are solved and the boundaries where the boundary conditions are imposed. This method is straightforward in derivation and simple in numerical implementation. As a diffuse interface approach, the SBM circumvents the need for structural meshing of the interfaces, which are difficult when the interfacial morphologies are complex. Thus, the SBM is a very powerful tool for image-based three-dimensional microstructural simulations. A variety of partial differential equations can be reformulated using the SBM, including those that govern mass transport, stress-strain responses, phase transformations, and electrochemistry. Validation tests are presented, and applications of the SBM will be demonstrated, including simulations based on experimentally obtained three-dimensional microstructures in energy materials. Speaker(s): Katsuyo Thornton (Materials Science and Engineering, University of Michigan)