The Unified-FFT Method for Fast Solution of Integral Equations as Applied to Shielded-Domain Electromagnetics

Electromagnetic (EM) solvers are widely used within computer-aided design (CAD) to improve and ensure success of circuit designs. Unfortunately, due to the complexity of Maxwell\u27s equations, they are often computationally expensive. While considerable progress has been made in the realm of speed-enhanced EM solvers, these fast solvers generally achieve their results through methods that introduce additional error components by way of geometric approximations, sparse-matrix approximations, multilevel decomposition of interactions, and more. This work introduces the new method, Unified-FFT (UFFT). A derivative of method of moments, UFFT scales as O(N log N), and achieves fast analysis by the unique combination of FFT-enhanced matrix fill operations (MFO) with FFT-enhanced matrix solve operations (MSO). In this work, two versions of UFFT are developed, UFFT-Precorrected (UFFT-P) and UFFT-Grid Totalizing (UFFT-GT). UFFT-P uses precorrected FFT for MSO and allows the use of basis functions that do not conform to a regular grid. UFFT-GT uses conjugate gradient FFT for MSO and features the capability of reducing the error of the solution down to machine precision. The main contribution of UFFT-P is a fast solver, which utilizes FFT for both MFO and MSO. It is demonstrated in this work to not only provide simulation results for large problems considerably faster than state of the art commercial tools, but also to be capable of simulating geometries which are too complex for conventional simulation. In UFFT-P these benefits come at the expense of a minor penalty to accuracy. UFFT-GT contains further contributions as it demonstrates that such a fast solver can be accurate to numerical precision as compared to a full, direct analysis. It is shown to provide even more algorithmic efficiency and faster performance than UFFT-P. UFFT-GT makes an additional contribution in that it is developed not only for planar geometries, but also for the case of multilayered dielectrics and metallization. This functionality is particularly useful for multi-layered printed circuit boards (PCBs) and integrated circuits (ICs). Finally, UFFT-GT contributes a 3D planar solver, which allows for current to be discretized in the z-direction. This allows for similar fast and accurate simulation with the inclusion of some 3D features, such as vias connecting metallization planes

Simulation of Spiral Slot Antennas on Composite Platforms

The project goals, plan and accomplishments up to this point are summarized in the viewgraphs. Among the various accomplishments, the most important have been: the development of the prismatic finite element code for doubly curved platforms and its validation with many different antenna configurations; the design and fabrication of a new slot spiral antennas suitable for automobile cellular, GPS and PCs communications; the investigation and development of various mesh truncation schemes, including the perfectly matched absorber and various fast integral equation methods; and the introduction of a frequency domain extrapolation technique (AWE) for predicting broadband responses using only a few samples of the response. This report contains several individual reports most of which have been submitted for publication to referred journals. For a report on the frequency extrapolation technique, the reader is referred to the UM Radiation Laboratory report A total of 14 papers have been published or accepted for publication with the full or partial support of this grant. Several more papers are in preparation

Applications of Adaptive Integral Method in Electromagnetic Scattering by Large-Scale Composite Media and Finite Arrays.

Ph.DDOCTOR OF PHILOSOPH

Electromagnetic simulations in frequency and time domain using adaptive integral method

Ph.DDOCTOR OF PHILOSOPH

Theoretical and experimental investigations of passive and integrated antennas

Ph.DDOCTOR OF PHILOSOPH

International Workshop on Finite Elements for Microwave Engineering

When Courant prepared the text of his 1942 address to the American Mathematical Society for publication, he added a two-page Appendix to illustrate how the variational methods first described by Lord Rayleigh could be put to wider use in potential theory. Choosing piecewise-linear approximants on a set of triangles which he called elements, he dashed off a couple of two-dimensional examples and the finite element method was born. … Finite element activity in electrical engineering began in earnest about 1968-1969. A paper on waveguide analysis was published in Alta Frequenza in early 1969, giving the details of a finite element formulation of the classical hollow waveguide problem. It was followed by a rapid succession of papers on magnetic fields in saturable materials, dielectric loaded waveguides, and other well-known boundary value problems of electromagnetics. … In the decade of the eighties, finite element methods spread quickly. In several technical areas, they assumed a dominant role in field problems. P.P. Silvester, San Miniato (PI), Italy, 1992 Early in the nineties the International Workshop on Finite Elements for Microwave Engineering started. This volume contains the history of the Workshop and the Proceedings of the 13th edition, Florence (Italy), 2016 . The 14th Workshop will be in Cartagena (Colombia), 2018

Accurate and efficient solutions of electromagnetic problems with the multilevel fast multipole algorithm

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 2009.Thesis (Ph.D.) -- Bilkent University, 2009.Includes bibliographical references leaves 434-226.The multilevel fast multipole algorithm (MLFMA) is a powerful method for the fast and efficient solution of electromagnetics problems discretized with large numbers of unknowns. This method reduces the complexity of matrix-vector multiplications required by iterative solvers and enables the solution of largescale problems that cannot be investigated by using traditional methods. On the other hand, efficiency and accuracy of solutions via MLFMA depend on many parameters, such as the integral-equation formulation, discretization, iterative solver, preconditioning, computing platform, parallelization, and many other details of the numerical implementation. This dissertation is based on our efforts to develop sophisticated implementations of MLFMA for the solution of real-life scattering and radiation problems involving three-dimensional complicated objects with arbitrary geometries.Ergül, Özgür SalihPh.D