# Using Modeling to Select the Type of Microwave Field Emitter for Dense-Layer Grain Dryers
## 2 Materials and Methods
### Methods  
The finite method was applied for the mathematical simulation. The finite integration technique (FIT) represents a method of spatial discretization designed for the computational solution of electromagnetic field problems in both time and frequency domains. It makes it possible to retain the basic topological properties of continuous equations such as conservation of charge and energy. The main idea of this approach is to apply the Maxwell equations in their integral form to a multilayer grid.  
\[\oint_{(\Gamma)}\left(H,\ dl\right)=\int_{(S)}\left(j+\frac{\partial D}{ \partial t}\right)dS, \tag{1}\]  
\[\oint_{(\Gamma)}\left(E,\ dl\right)=-\int_{(S)}\left(\frac{\partial B}{ \partial t}\right)dS, \tag{2}\]  
\[\oint_{(S)}\left(D,\ dS\right)=\int_{V}\rho dV, \tag{3}\]  
\[\oint_{(S)}\left(B,\ dS\right)=0, \tag{4}\]  
where \(E\) is electric field intensity (V/m),  
\(H\) is magnetic field intensity (A/m),  
\(B\) is magnetic induction (T),  
\(D\) is electric induction (Coulomb/m\({}^{2}\)),  
\(\Gamma\) is borderline enclosing a free-form surface (m\({}^{2}\)),  
\(S\) is free-form surface (m\({}^{2}\)),  
\(V\) is volume (m\({}^{3}\)),  
\(j\) is electric current density (A/m\({}^{3}\)),  
\(l\) is closed contour (m),  
\(\rho\) is electric charge density (Coulomb/m\({}^{3}\)), and  
\(t\) is time (s).  
The major advantages of this method include high flexibility in geometric modeling and boundary processing, and the possibility to involve any material distribution and properties of the material. Additionally, the application of a correlated binary orthogonal grid in combination with an explicit integrating scheme in time yields effective algorithms in terms of the simulation process and storage efficiency.  
The essence of the method is based on tiling the computational domain into a finite number of spatial cells. The cells are built so that they completely fit together, and the intersection of two different cells is either a void or a polygon with a one-dimensional edge, or a point shared by both cells (Figure 5).  
Such a partitioning scheme yields the final integration grid that is used as the computation array. Therefore, the entire computation domain is composed of a finite number of elementary cells. Variable electromagnetic fields and flows are normally located along the elementary lines or elementary planes. Similarly, intensities directed along other edges of the cell can be calculated. The aggregate magnetic flow through a plane can be determined as the integral of the magnetic flow density through this plane. As a result, electric field  
Figure 5: Example of tiling the space in the waveguide output into cells.  
densities and magnetic flows of the entire cell complex are represented in a matrix form. The solution of this equation yields the desired variables.  
In the process of designing microwave devices with the help of CST Microwave Studio 2019 design, structures in a three-dimensional representation are produced by drawing simplest geometric forms (primitives) and by performing logic (Boolean) operations over them [28]. The effectiveness of radiators was evaluated with the use of the following indicators:  
* Standing wave ratio (SWR) making it possible to evaluate radiator coherence;
* Radiation efficiency characterizing the share of energy transferred through the waveguide from magnetron;
* Angular pattern of the microwave field. Radiation directionality diagram is drawn in 3D form, which makes it possible to evaluate uniformity of the electromagnetic field distribution in the radiator output;
* The radiation pattern of the microwave field along the waveguide is perpendicular to the radiation;
* Radiated microwave power distribution.