**1. Introduction**

The finite element method (F.E.M.) is a numerical procedure that can be applied to solve various problems in engineering and science. In general, this method is used to solve steady, transient, linear, and nonlinear problems in electromagnetics, structural analysis, and fluid dynamics [1]. The finite element method has the main advantage of being able to handle all kinds of geometries and non-homogeneous materials without the need to change computer code formulations. The idea of this method is to break the problem into a large number of areas, each with simple geometry to facilitate problem-solving. As a result, the domain breaks down into a number of small elements, and the problem goes from small but challenging to solve into large and relatively easy to solve. Through the process of discretization, linear algebra problems are formed with many unknowns. In the case of electromagnetics, a discretization scheme, as implied by F.E.M., which implicitly combines most of the theoretical features of the problem analyzed is the best solution for obtaining accurate results in problems with complex, nonlinear geometries, etc. [2, 3]. This method can also be used for complex differential equations that are very difficult to solve. In the case of electromagnetic or magnetic fields, the finite element method is also known as FEMM.

FEMM is a suite of programs for solving low-frequency electromagnetic problems on two-dimensional planar and axisymmetric domains. The program currently addresses linear/nonlinear magnetostatic problems, linear/nonlinear time-harmonic magnetic problems, linear electrostatic problems, and steady-state heat flow problems. In the problem of this method, there are generally three parts to the problem [4].

Interactive shell program is a Multiple Document Interface pre-processor and a post-processor for various types of problems that are solved by FEMM. This case is a CAD-like interface for laying out the geometry of the problem to be solved and for defining material properties and boundary conditions [5]. The program also allows the user to inspect a field at specific points, as well as evaluate several different integrals and plot varying amounts of interest along with a user-defined contour [6]. Triangle breaks down the solution region into a large number of triangles, a vital part of the finite element process. Furthermore, Solvers, each solver takes a set of data files that describe problems and solves the relevant partial differential equations to obtain values for the desired field throughout the solution domain [7].

Finite Element Method Magnetics (FEMM) software has been developed for reasons of dealing with some of the limiting cases of Maxwell equations. The magnetic problem that is handled can be considered as a low frequency (L.F.) problem. In some cases, this problem can ignore displacement currents. This program discusses 2D planar and 3D axisymmetric linear and nonlinear harmonic magnetic, magnetostatic, and linear electrostatic problems [8].

Computer-assisted field distribution analysis for electromagnetic devices or component performance has become a simple, profitable, and fast method with good accuracy [9]. The magnetic field calculation problem aims to determine the value of one or more unknown functions, such as magnetic field intensity, magnetic flux density, scalar magnetic potential, and magnetic vector potential.

From a mathematical point of view, Maxwell equations can generally explain physical electromagnetic phenomena. Specifically, this point of view is a differential equation with specific boundary conditions. With this method, the correct solution to the problem is obtained. It is an analytical method that can be used to solve problems [10]. Analytical methods (method of appropriate representation, method of variable separation) are often applied to solve relatively simple problems. However, the problems that occur in practice are sometimes more complex regarding loading conditions, boundary conditions, geometric construction, and material heterogeneity, so that the integration of differential equations is challenging to solve by analytical methods. Therefore, the analytic solution can only be done by making a simplified model that allows the integration of the differential Equations [11]. Sometimes it is better to come up with a more realistic estimate of the value, rather than a precise solution from a simplified model. The approximate solution by the finite element method obtained by the numerical method reflects reality better than the exact solution of the simplified model [12].

Specific forms of electromagnetic field law for static magnetic fields are overcome by considering solving the magnetic problem through FEMM. Some of them are considering the model of the relationship between magnetic induction and the intensity of its magnetic field, the enunciation of static magnetic fields, passing conditions through discontinuity surfaces, enunciation of scalar magnetic potential magnetostatic field problems and enunciation using magnetic vector potentials [13]. Some geometric configurations conform to the general formula for the unique conditions of a particular shape. The solution to this problem also depends on the relationship between magnetic intensity and magnetic field induction, the choice of material types such as linear and non-isotropic materials, linear and isotropic

#### *Finite Element Magnetic Method for Magnetorheological Based Actuators DOI: http://dx.doi.org/10.5772/intechopen.94223*

materials, nonlinear and non-isotropic materials with hysteresis, and nonlinear and isotropic materials, without permanent magnetization [14].

In other cases, such as in the development of magnetorheological devices (dampers, brakes, mounting, etc.), FEMM is used to solve the problem of magnetic flux density. Using the help of FEMM, solving magnetic problems can be solved quickly. The magnetic flux density, which is complex and challenging to be solved by numerical methods, can be determined by simulating the FEMM by using the material properties data to obtain the magnitude of the magnetic flux density. The simulation results are then used to determine the predicted values such as the pressure difference (in the case of the damper valve) using numerical or calculation methods [15].
