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This book covers the topic of multiphysics simulation with a focus on electromechanical systems (e.g. electronics, motors, and actuators). The importance of electromechanical systems is that they are becoming more prevalent in modern energy storage/transmission devices plus advanced vehicles. Thus, the emphasis of the first part of the book is to provide a review of governing equations and numerical methods necessary for the multiphysics analysis of such systems. Representative electromechanical 2D and 3D example studies are then provided. The focus of the second part of the book is the integration of optimization (primarily gradient-based and some parametric) methods into the simulation process for efficient system design. Thus, the book highlights the unique intersection of modern computer-aided modeling and simulation tools with increasingly relevant numerical optimization techniques and how the combination leads to novel designs with improved performance.