**5. Simulation Software**

Several core loss models have been reviewed; they are the base for developing a series of numerical and theoretical models that are useful for designing magnetic components. Nonetheless, they fail to predict dynamic magnetic behaviors. Usually, the calculation of the core parameters' losses in a dynamic situation is complicated (specially with complex geometries), and it requires a rigorous numerical treatment [126].

Several methods are used in the simulation and calculation of core and wire windings. However, the finite element method (FEM) is the most widely used for designs in 2-D and 3-D [22].

In 1960 Clough introduced the name of Finite Element Method (FEM), which continues to these days [127]. FEM is a computational method whose basic idea consists on finding a complicated problem and replacing it with a simpler one. It is always possible to improve the approximation solution spending more computational effort [127,128].

To find the solution of a region, the FEM considers that it is built of many small, interconnected subregions called elements [128], and the global solution is obtained from the union of individual solutions on these regions [129].

The FEM is a tool for solving problems with partial differential equations that are part of physics problems [130]. FEM has quite benefits of using it; some of them is the freedom that it offers in the discretization's selection, and its well developed theoretical base that allows valid error estimates for the numerical model equations, and its flexibility to be adapted to a wide range of numerical problems [129,131].

The FEM was originally developed to solve problems in solid-state mechanics. Still, its versatility, excellent simulation technique, availability to optimize the mesh size, and accuracy have been implemented in a wide variety of applied science and engineering [127,129].

Mathematical models are discretized by FEM, resulting in numerical models. To solve the discretized equations, Finite Element Analysis (FEA) is used [131,132].

There are many FEM software developers in the market; however, Ansys® is the leader so far. Ansys, Inc. (Canonsburg, PA, USA) was founded in 1970s, and since then, it has developed, commercialized and brought support at several range of physics through engineering simulation software. The Ansys® catalogue includes simulation software for semiconductors, structures, materials, fluids, and electronics.

An exciting tool that Ansys has developed in recent years is Twin Builder®, a multitechnology platform to create digital representations simulations, recollected real-time data information through sensor inputs asset with real-world [133]. Twin Builder® is a powerful and robust multi-domain system modelling compatible with a series of standard languages and formats as SPICE, Python, C/C++, simplorer modelling language (SML), among others. It can be used to develop basic simulation experiments and advanced simulation studies, from 2-D and 3-D physics simulations . Inclusive the functional mock-up interface (FMI standard) can import and export models as available mockup units (FMU). An example of an electromagnetic digital twin is shown in Figure 5. Twin Builder® only is compatible with Ansys software and its main application is in the industry as virtual laboratory to test any kind of system.

**Figure 5.** Twin Builder example.

Added to these FEM software developers, there is Comsol Multiphysics®, which is a powerful software tool for developing and simulating modelling designs in all fields of engineering, manufacturing, and scientific research [134]. This software was founded in 1986. Its main characteristic is its friendly graphical user interface. The Comsol Multiphysics® community is more significant than the other software. In Figure 6, two simulations are provided. Comsol Multiphysics® can import designs in CAD and export final designs to Simulink®, given that both belong to the MathWorks® family. Comsol Multiphysics® is oriented to students and academic researchers, it is not complex to learn and it is an excellent option to start with for FEM software.

**Figure 6.** Examples of magnetic flux density simulations' in Comsol Multiphysics for a powder core with shape: (**a**) toroidal , and (**b**) "E".

Another big company of FEM software is JMAG®, a simulation software specialized for electric device design and development, including the accurate model of complex magnetic phenomena. It was founded in 1983, and currently, its most attractive feature is the capability to link various systems through its interface [135].

The JMAG® interface allows the data exchange at high speed without loss of precision with other software as SPEED, PSIM and MATLAB/Simulink; one example of this software is shown in Figure 7. Additionally, JMAG® allows to the user import and export multipurpose files and to run VB Script and other scripting languages [135].

**Figure 7.** JMAG example of magnetic flux density simulation.

Another feature of JMAG® is its CAD interface to link and import files with software as SOLIDWORKS, CATIA V5, among others to test the model developed using software in the loop (SIL), model in the loop (MIL) and hardware in the loop (HIL) systems, which are applied for system-level and real-time simulations [135,136]. JMAG® is a specialized software to model inductors and magnetic motors adding vibration and thermal analysis; however, the information about it is limited, and it is complex to learn.

The software mentioned before are the most commonly used; however, there are many other finite element software packages available to any platform and they have different features [137].
