This chapter begins with a motivation to use computational models in scientific and technical applications. An overview of the advantages and drawbacks of numerical simulations with respect to laboratory experiments is given and advancements in various fields are discussed.

After this general introduction, a historical overview of the subject is presented and the present state of the art is discussed. In particular, it is shown that immersed boundary methods are being used in all fields of computational science and the number of scientific publications per year has been increasing with a constant acceleration over the past two decades: This has resulted in an exploding research field in which a reference textbook is still missing.

Finally, the objective of the book and the plan of the various chapters is given.

Various feeding techniques and antenna structures for achieving dual-polarized and circularly polarized ME dipoles will be reviewed. Since some circularly polarized ME dipoles can be developed from dual-polarized ME dipoles, these two classes of ME dipoles are considered and reviewed together here.

The development of linearly polarized magnetoelectric (ME) dipoles operated at lower microwave frequencies is reviewed. Magnetoelectric dipoles can be fabricated at low costs, as they are purely made of metal plates at a few GHz range. Designs with modified L-shaped probe feeds for various purposes are first presented. Magnetoelectric dipoles with modified dipole shapes and feeds for enabling the antennas to be d.c. grounded are summarized. The aperture coupling technique was widely applied for the designs of microstrip antennas. Magnetoelectric dipoles with aperture-coupled feeds were also proposed in the literature. Their characteristics are presented. Differentially fed ME dipoles are also reviewed. The performance of ME dipoles for MIMO systems is discussed, which is of topical interest for 5G applications. Some recent applications of linearly polarized ME dipoles in different array environments are also presented.

As IBMs have gained popularity, their use has expanded to multiphysics problems in which the Navier-Stokes equations are only one among many other possibilities. In this chapter, a list of advanced applications is described in which IBMs are used to solve heat transfer, phase change and chemical reaction problems. These examples are intended as suggestions to extend the application of immersed boundary methods to complex physics problems.

The various forcing strategies to be implemented in the governing equations are described in this chapter. Two big categories are first introduced, namely continuous forcing and discrete forcing methods. The various techniques are then detailed and the steps needed to implement them into an existing flow solver are described.

As any immersed boundary method has to be coupled with a solution algorithm for the governing equations, pseudo-compressibility and fractional-step methods are described in detail and some issues related to their combination with IBMs illustrated.

With this chapter, the technical part of immersed boundary methods is initiated. Here it is explained how to define in the most convenient way a complex geometry object and how, after having immersed it in a computational grid, it is possible to determine the position (tagging) of the Eulerian nodes with respect to the boundary of the body.

Several computational geometry theorems are used to design an efficient computational algorithm which makes possible the tagging step within limited CPU time even when the computational grid contains tens of millions of nodes and the immersed object is described by hundreds of thousands of elements. This efficiency is key in problems involving moving bodies, deformable objects or fluid-structure interaction problems.

A comprehensive review on using different transmission lines for feeding ME dipole antennas and arrays is presented, including the SIW, ridge gap waveguide, packaged microstrip line, and substrate-integrated coaxial line feeds. In addition, the developments of low profile of ME dipole arrays, filtering ME dipoles, and all-metal ME dipole arrays for high-power applications are summarized. Some other recent applications are briefly reported. Hopefully, our readers can appreciate the attractiveness of the ME dipoles for future wireless applications at millimeter-wave and terahertz frequencies.

This chapter is devoted to the application of IBMs to problems with moving boundaries. Specific adaptations of the algorithms are needed in order to cope with the Eulerian nodes at the interface that change position from inside to outside the body within one time step.

In turn, the boundary reconstruction of the solution is also affected and the necessary changes to the method are described.

In this chapter it is explained how to compute the hydrodynamic loads produced by pressure and viscous stresses over an immersed surface. Several procedures are illustrated that entail different computational costs and degree of precision. The choice depends on whether only the resultant of the forces is needed or if the local values of the loads are needed. Finally, a simple validation of the discussed methods for a body with prescribed kinematics is shown.

This chapter introduces control schemes based on the PT-symmetric wireless power transfer (WPT) system. It begins with an overview of PT symmetry and its relevance to WPT, followed by detailed models and analyses based on circuit theory and coupled-mode theory. The chapter explores the output characteristics of PT-symmetric systems and presents control methods for optimizing output power through load identification. Experimental results are provided to validate the proposed control schemes, demonstrating their effectiveness in managing power transfer and enhancing system performance. The chapter highlights the innovative aspects of PT-symmetric WPT and its potential applications.