Rautio, Brian J.
The Unified-FFT Method for Fast Solution of Integral Equations as Applied to Shielded-Domain Electromagnetics.
Degree: PhD, Electrical Engineering and Computer Science, 2014, Syracuse University
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's 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.
Advisors/Committee Members: Jay K. Lee, Vladimir I. Okhmatovski.
Subjects/Keywords: Computational Electromagnetics; Computational Methods; Fast Algorithms; Fast Methods; Method of Moments; Numerical Electromagnetics; Engineering
to Zotero / EndNote / Reference
APA (6th Edition):
Rautio, B. J. (2014). The Unified-FFT Method for Fast Solution of Integral Equations as Applied to Shielded-Domain Electromagnetics. (Doctoral Dissertation). Syracuse University. Retrieved from https://surface.syr.edu/etd/167
Chicago Manual of Style (16th Edition):
Rautio, Brian J. “The Unified-FFT Method for Fast Solution of Integral Equations as Applied to Shielded-Domain Electromagnetics.” 2014. Doctoral Dissertation, Syracuse University. Accessed October 22, 2019.
MLA Handbook (7th Edition):
Rautio, Brian J. “The Unified-FFT Method for Fast Solution of Integral Equations as Applied to Shielded-Domain Electromagnetics.” 2014. Web. 22 Oct 2019.
Rautio BJ. The Unified-FFT Method for Fast Solution of Integral Equations as Applied to Shielded-Domain Electromagnetics. [Internet] [Doctoral dissertation]. Syracuse University; 2014. [cited 2019 Oct 22].
Available from: https://surface.syr.edu/etd/167.
Council of Science Editors:
Rautio BJ. The Unified-FFT Method for Fast Solution of Integral Equations as Applied to Shielded-Domain Electromagnetics. [Doctoral Dissertation]. Syracuse University; 2014. Available from: https://surface.syr.edu/etd/167