## Daniel Weile, Associate Professor

### Research Interests

Prof Weile's research focuses on the numerical analysis and design of electromagnetic devices

**Electromagnetics** is the field of physics that deals with the propagation, transmission, and scattering of light, radio waves, and microwaves. Electromagnetic devices are among the most recognizable and important of the information age: antennas, transmission lines, and generators are among the most common. All of these various technologies are governed by a set of law's known as Maxwell's Equations.

**Computational electromagnetics** is the science and art of solving Maxwell's Equations accurately and efficiently on a computer. (The application of computation electromagnetics most familiar to the public was the design of the stealh bomber.) While in principle there are to solve Maxwell's Equations numerically, Prof. Weile's research focuses primarily on the solution of integral equations and time-domain integral equations (TDIEs). TDIEs are especially interesting because they have important applications (such as the control of electromagnetic interference), but have proven difficult to solve accurately and efficiently. Indeed, most initial attempts at solving TDIEs were unstable, and drowned the desired solution in a deluge of error.

Of course, the goal of any engineer is design, and analysis is only the first step. Of specific interest here is automated design, using evolutionary computation techniques like genetic algorithms, genetic programming, and particle swarm optimization. These techniques are based on simulating optimization processes in nature (Darwinian evolution and social interactions) and tend to be better than traditional techniques at solving complicated, multimodal optimization problems. Current work focuses on improving the efficiency of these algorithms, as well as making them more creative by broadening their applicability.

**Time-domain integral equation methods for the solution of Maxwell's Equations**

While methods for solving Maxwell equations on computers have existed since the late 1960s, most work has concentrated on three techniques: the method of moments (MoM), the finite element method (FEM), and the Finite Difference Time Domain Method (FDTD). These methods differ depending on whether they solve differential or integral equations, and on whether they work in the time or frequency domain. Time domain integral equations (TDIE) methods, though known for just as long, have had historical problems with efficiency and stability and so have been ignored. However, TDIEs are important because in principle they offer the best method for approaching certain classes or important problems involving electromagnetic interference or microelectromechanical structures. Thus, Prof. Weile's group is investigating accurate and efficient methods for solving the time domain integral equations of electromagnetics.

### Related Publications

G. Pisharody and D. S. Weile, "Electromagnetic scattering from homogeneous dielectric bodies using time-domain integral equations," *IEEE Trans. Antennas Propagat.*, vol. 54, no. 2, pp. 687-697, **2006**.

R. A. Wildman and D. S. Weile, "Two-dimensional transverse-magnetic time-domain scattering using the Nystrom method and bandlimited extrapolation," *IEEE Trans. Antennas Propagat.*, vol. 53, no. 7 , pp. 2259-2266, **2005**.

A. Mohan and D. S. Weile, "Accurate modelling of the cylindrical wire kernel," *Microwave and Optical Technology Letters*, vol. 48, no. 4, pp. 740-744, **2006**.