Prof. Francisco Saez de Adana, Department Of Computer Science, Universidad de Alcala, Spain.


The asymptotic techniques have been widely used for solving electromagnetic problems when the electrical size of the scenario is large in comparison to the wavelength. These techniques are applied to problems such as the analysis of on-board antennas, computation of the RCS, antenna design or the study of the propagation in mobile communications. However, the accuracy of these techniques is related to the fidelity of the geometrical modeling compared to the real scenario. There are two options. The first option is a simplification of this modeling using canonical structures to simplify the geometrical treatment associated with these techniques. The disadvantage of this option is a loss of accuracy in the results. The second option is an exact modeling of the scenario in order to obtain results that are as accurate as possible. In this case, the price to pay is the computational cost associated with the solution of the problem. This tutorial attempts to show how this second modelling option can be applied to obtain very accurate results; combining the electromagnetic techniques with some geometrical techniques enables the solution of realistic and complex problems with a reasonable amount of computational resources.

With this aim, the tutorial presents the application of high frequency or asymptotic techniques to the analysis of complex electromagnetic problems. By complex problems we refer to those that are completely arbitrary in shape. A suitable geometrical modeling of the problem is then needed. This modeling is performed by means of parametric surfaces called NURBS (Non Uniform Rational B-Splines) that are commonly used in the world of Computer Aided Graphic Design for aeronautical and architectural applications. A description of this modeling is included in the tutorial. The main objective of the tutorial is the application of the asymptotic techniques to the analysis of problems modeled by these kind of surfaces. Two techniques are described: the Uniform Theory of Diffraction (UTD) and the Physical Optics (PO). The basic theory of both techniques is explained but with special focus on their applicability to objects modeled by NURBS. A section is also dedicated to the so-called ray-tracing acceleration techniques which are very important for addressing complex problems with a reduced computational cost. The application of these techniques to both UTD and PO are included in the tutorial. 

  • Structure:

    Chapter 1. Introduction

    This chapter is an introduction to the asymptotic techniques and their application to electromagnetic problems in real, complex scenarios. The existing numerical methods are summarized, and the motivation for their application to these kind of problems is shown.

    Chapter 2. Geometrical model. NURBS surfaces

    This chapter explains why good geometrical modeling is needed for the application of asymptotic techniques to realistic problems. The previous techniques are introduced as a rationale for the selection of the most suitable technique for these applications: the arbitrary shaped parametric surfaces known as the Non Uniform Rational B-Splines Surfaces (NURBS).


    2.1. Introduction. Modeling techniques.

    2.2. Bezier Curves

    2.3. Bezier Surfaces

    2.4. Rational B-Spline Surfaces

    2.5. NURBS Surfaces

    Chapter 3. Geometrical Optics and Uniform Theory of Diffraction (GO/UTD)


    This chapter explains the foundations of the GO/UTD and the ray-tracing theory. The general GO/UTD formulation will be introduced, but special emphasis will be given to the determination of the ray trajectories, especially when the bodies are modeled by NURBS.

    3.1. Introduction

    3.2. GO/UTD Electromagnetic Formulation

    3.2.1. Direct Ray

    3.2.2. Reflected Ray

    3.2.3. Diffracted Ray

    3.2.4. Creeping Waves

    3.2.5. Multiple effects

    3.3. Ray-Tracing

    3.2.1. Determination of the ray trajectories

    3.2.2. The shadowing problem


    Chapter 4. Physical Optics and Physical Theory of Diffraction(PO/PTD)

    This chapter explains the basic formulation of the PO/PTD, and the numerical methods used to compute the PO/PTD integrals, including the Stationary Phase Method (SPM). As in the previous chapter, special emphasis will be given to the computation of these integrals when the bodies are modeled by NURBS.

    4.1. Introduction

    4.2. Physical Optics foundations

    4.3. Integration techniques used to compute the PO integral

    4.4. The Stationary Phase Method

    4.5. Multiple reflections using PO

    4.6. Physical Theory of Diffraction.

    Chapter 5. Acceleration techniques

    This chapter is dedicated to the acceleration techniques that are used to reduce the computational cost of the ray-tracing calculation. In the first section, two techniques will be discussed: the Angular Z-Buffer and Space Volumetric Partitioning and its application to direct ray computation. The following sections will explain the application of these acceleration techniques to the computation of the ray-trajectories for multiple order effects.

    5.1. Introduction

    5.2. Ray-Tracing acceleration techniques

    5.2.1 Angular Z-Buffer technique

    5.2.2 Space Volumetric Partitioning

    5.3. Application of the Acceleration techniques to the calculation of the ray-trajectories

    5.3.1. Reflected rays

    5.3.2. Diffracted rays

    5.3.4. Multiple order rays

    5.5. Application of the acceleration techniques to the reduction of the computational cost associated with the computation of the PO/PTD integrals

    Chapter 6. Applications

    Practical applications of the previous methods to realistic cases will be described in this chapter. The different cases will be studied in detail, with comparisons of simulated and measured results, computational cost, etc. 

    6.1. Introduction

    6.2. Radar Cross section applications

    6.3. On-board antenna applications

    6.4. Radiopropagation in indoor and outdoor applications

    6.5. Antenna Design applications


About the Presenter

Francisco Saez de Adana was born in Santander, Spain, in 1972. He received the BS, MS and PhD. degrees in Telecommunications Engineering from the University of Cantabria, Spain, in 1994, 1996 and 2000, respectively. Since 1998 he works at the University of Alcala, first as assistant professor and since 2011 as professor. He has worked as faculty research at Arizona State University from March 2003 to August 2003. He has participated in more than forty research projects with Spanish, European, American and Japanese companies and universities, related with analysis of on board antennas, radio propagation in mobile communication, RCS computation, etc. He has directed four Ph. D. Dissertations, has published more than thirty papers in referred journals and more than 60 conference contributions at international symposia. His research interests are in areas of high-frequency methods in electromagnetic radiation and scattering, onboard antennas analysis, radio propagation on mobile communications and ray-tracing acceleration techniques.