**1. Introduction**

Signal propagation underground and in soil medium constitute the backbone of the Internet of underground things (IoUT), which power many applications such as precision agriculture, border monitoring for intrusion detection, pipeline monitoring, etc. [1–3]. In the recent past, the study of signal propagation in soil medium for underground wireless communication has focused mainly on empirical techniques [4–8]. The most commonly used modeling techniques for implementing IoUT include electromagnetic waves, magnetic induction, and acoustic waves [9, 10]. Electromagnetic field analysis is performed in this chapter using numerical modeling with the finite element method to examine the signal strength in the soil medium.

The process of numerical modeling of how electromagnetic fields propagate and interact with physical objects and the environment is usually referred to as computational electromagnetics (CEM), numerical electromagnetics. The primary

motivation of this process is to develop efficient approximations to Maxwell's equations through numerical schemes for cases where closed-form analytical solutions of Maxwell's equation cannot be obtained due to the complexity of geometries, material parameters, and boundary conditions. Therefore, several real-life problems that are not analytically computable, such as electromagnetic scattering, antenna radiation, electromagnetic wave propagation, electromagnetic compatibility, etc., can effectively be solved by numerical techniques. The mathematical model of the electromagnetic problem is usually obtained in terms of partial differential equations, integral equations, or integro-differential equations derived from Maxwell's equations and a set of a priori constraints of the problem such as boundary and initial conditions material parameters and geometry. The problem is ideally defined on an infinite-dimensional function space. Numerical methods apply a discretization to the continuum to reduce infinite degrees of freedom to a finite degree of freedom. In other words, the solution of an infinite dimensiondimensional problem is projected into a finite-dimensional space. Hence, the solution to the problem becomes amenable on a digital computer. The main philosophy in most of the numerical methods is to apply the divide-and-conquer strategy. The idea is to divide an intractable continuous problem into smaller pieces (divide), express the solution over each small piece (conquer), and then combine the piecewise solutions to obtain a global solution. In this chapter, FEM will be applied to the two-dimensional boundary value problem in EM wave propagation through the soil to evaluate the signal strength of the wave propagation in soil. This evaluation will be based on the incidence angle of the transmitted wave. The radar cross-section of the scatterer will be used to evaluate the direction of the wave.
