Electromagnetic Fields (EMFs) have been studied and used for a long time. The past decades have seen a tremendous increase of applications of EMF in daily life. A particularly prevalent application is formed by wireless personal communication devices, e.g., mobile phones with currently more than five billion users worldwide. Large efforts have been expended to develop tools and methods that can be used to design EMF systems, to manage their performance, capabilities, quality, efficiency, compatibility, as well as to ensure that they comply with safety standards. Taking advantage of improvements in computer performance, efficient numerical methods continue to be developed that are being used to predict or characterize the EMF. In addition, particularly significant advances in software implementation and in experimental setups and techniques have been achieved during the past 15 years. Today, computers are capable of handling physically and electrically large problems, almost without limitations, thanks to distributed computing. Numerical methods such as FDTD (Finite-Difference Time-Domain) have been improved and adapted to allow for accurate estimation of EMFs in complex structures. On the experimental side, reverberation chambers have been studied and appear to be well suited to study various applications in electromagnetic compatibility and beyond. Most, if not all, numerical and experimental methods and simulation tools have been designed mainly with a view to solve deterministic problems. In a mathematical framework, these can be defined as well-posed problems, characterized by differential equations for single-mode systems furnished with a complete set of fixed initial and boundary conditions. However, increasingly complex systems need to be handled and solved nowadays, in which one or more of the system parameters or boundary conditions may be ill-defined, i.e., be either unknown or fluctuating in a quasi-random manner, particularly for multi-mode dynamic systems. In addition to an estimate for the solution, a quantitative evaluation and statement of the associated uncertainty in the knowledge of the field quantity of interest is then called for. Computers that are capable of solving deterministic problems with millions of unknowns can provide only approximate solutions to a real physical process, but they cannot handle complex real-life scenarios involving uncertainty. On the other hand, in a physical experiment, the process output can be observed when the input is varying due to uncertainties. In other words, the uncertainties of the system's input parameters “drive” those in the output field variables. Therefore, new approaches to numerical simulation are called for. Worldwide efforts are currently carried out in numerical as well as in experimental approaches in an effort to manage this situation through fusion of experimental, analytical, and statistical–physical methods of characterization. For example, geostatistics are being used to estimate J. Wiart (*) WHIST Lab, Orange Lab, 38 40 rue du General Leclerc, 92794 Issy les Moulineaux Cedex, France e-mail: joe.wiart@orange-ftgroup.com
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