Novel Frequency Domain Techniques and Advances in Finite Difference Time Domain (FDTD) Method for Efficient Solution of Multiscale Electromagnetic Problems

Open Access
Author:
Panayappan, Kadappan
Graduate Program:
Electrical Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
March 01, 2013
Committee Members:
  • Raj Mittra, Dissertation Advisor
  • Dr James Breakall, Committee Member
  • Douglas Henry Werner, Committee Member
  • Michael T Lanagan, Committee Member
Keywords:
  • Computational Electromagnetics
  • Multiscale Problems
  • FDTD
  • Conformal FDTD
  • RUFD
  • DM Approach
  • Low Frequency
  • Numerical Methods
Abstract:
With the advent of sub-micron technologies and increasing awareness of Electromagnetic Interference and Compatibility (EMI/EMC) issues, designers are often interested in full- wave solutions of complete systems, taking to account a variety of environments in which the system operates. However, attempts to do this substantially increase the complexities involved in computing full-wave solutions, especially when the problems involve multi- scale geometries with very fine features. For such problems, even the well-established numerical methods, such as the time domain technique FDTD and the frequency domain methods FEM and MoM, are often challenged to the limits of their capabilities. In an attempt to address such challenges, three novel techniques have been introduced in this work, namely Dipole Moment (DM) Approach, Recursive Update in Frequency Domain (RUFD) and New Finite Difference Time Domain (νFDTD). Furthermore, the efficacy of the above techniques has been illustrated, via several examples, and the results obtained by proposed techniques have been compared with other existing numerical methods for the purpose of validation. The DM method is a new physics-based approach for formulating MoM problems, which is based on the use of dipole moments (DMs), as opposed to the conventional Green’s functions. The absence of the Green’s functions, as well as those of the vector and scalar potentials, helps to eliminate two of the key sources of difficulties in the conventional MoM formulation, namely the singularity and low-frequency problems. Specifically, we show that there are no singularities that we need to be concerned with in the DM formulation; hence, this obviates the need for special techniques for integrating these singularities. Yet another salutary feature of the DM approach is its ability to handle thin and lossy structures, or whether they are metallic, dielectric-type, or even combinations thereof. We have found that the DM formulation can handle these types of objects with ease, without running into ill-conditioning problems, even for very thin wire-like or surface-type structures, which lead to ill-conditioned MoM matrices when these problems are formulated in the conventional manner. The technique is valid over the entire frequency range, from low to high, and it does not require the use of loop-star type of basis functions in order to mitigate the low frequency problem. Next, we have introduced the RUFD, which is a general-purpose frequency domain technique, and which still preserves the salutary features of the time domain methods. RUFD is a frequency domain Maxwell-solver, which neither relies upon iterative nor on inversion techniques. The algorithm also preserves the advantages of the parallelizability—which is a highly desirable attribute of CEM solvers—by using the difference form of Maxwell’s equations. Since RUFD solves the Maxwell’s equations in a recursive manner, without using either iteration or inversion, the problems of dealing with ill-conditioned matrices, or constructing robust pre-conditioners are totally avoided. Also, as a frequency domain solver, it can handle dispersive media, including plasmonics, relatively easily. The conventional time domain technique FDTD demands extensive computational resources when solving low frequency problems, or when dealing with dispersive media. The νFDTD (New FDTD) technique is a new general-purpose field solver, which is designed to tackle the above issues using some novel approaches, which deviate significantly from the legacy methods that only rely on minor modifications of the FDTD update algorithm. The νFDTD solver is a hybridized version of the conformal FDTD (CFDTD), and a novel frequency domain technique called the Dipole Moment Approach (DM Approach). This blend of time domain and frequency domain techniques empowers the solver with potential to solve problems that involve: (i) calculating low frequency response accurately and numerically efficiently; (ii) handling non-Cartesian geometries such as curved surfaces accurately without staircasing; (iii) handling thin structures, with or without finite losses; and (iv) dealing with multi-scale geometries.