The safety of complex engineered systems and critical infrastructures are important to ensure society's industrial and economic prosperity, advances in complex systems computation and modeling is always greatly desired. Challenges still remain in applications such as large-scale sensing and monitoring of those systems to ensure the structural heath. This paper proposed a novel and fast imaging and modeling mechanism using an optimized fast multipole method with accelerated Cartesian expansion that can significantly reduce the electromagnetic (EM) field calculation, data acquisition and analysis time. Two examples were discussed including defect sensing and a rigorous derivation of error bound in EM imaging. New formulations to simplify the Green's function, the Generalized Maxwell Expansion were also introduced and implemented.