Combined fast multipole-QR compression technique for solving electrically small to large structures for broadband applications

An approach that efficiently solves for a desired parameter of a system or device that can include both electrically large fast multipole method (FMM) elements, and electrically small QR elements. The system or device is setup as an oct-tree structure that can include regions of both the FMM type and the QR type. An iterative solver is then used to determine a first matrix vector product for any electrically large elements, and a second matrix vector product for any electrically small elements that are included in the structure. These matrix vector products for the electrically large elements and the electrically small elements are combined, and a net delta for a combination of the matrix vector products is determined. The iteration continues until a net delta is obtained that is within predefined limits. The matrix vector products that were last obtained are used to solve for the desired parameter

Technique for Solving Electrically Small to Large Structures for Broadband Applications

Fast iterative algorithms are often used for solving Method of Moments (MoM) systems, having a large number of unknowns, to determine current distribution and other parameters. The most commonly used fast methods include the fast multipole method (FMM), the precorrected fast Fourier transform (PFFT), and low-rank QR compression methods. These methods reduce the O(N) memory and time requirements to O(N log N) by compressing the dense MoM system so as to exploit the physics of Green s Function interactions. FFT-based techniques for solving such problems are efficient for spacefilling and uniform structures, but their performance substantially degrades for non-uniformly distributed structures due to the inherent need to employ a uniform global grid. FMM or QR techniques are better suited than FFT techniques; however, neither the FMM nor the QR technique can be used at all frequencies. This method has been developed to efficiently solve for a desired parameter of a system or device that can include both electrically large FMM elements, and electrically small QR elements. The system or device is set up as an oct-tree structure that can include regions of both the FMM type and the QR type. The system is enclosed with a cube at a 0- th level, splitting the cube at the 0-th level into eight child cubes. This forms cubes at a 1st level, recursively repeating the splitting process for cubes at successive levels until a desired number of levels is created. For each cube that is thus formed, neighbor lists and interaction lists are maintained. An iterative solver is then used to determine a first matrix vector product for any electrically large elements as well as a second matrix vector product for any electrically small elements that are included in the structure. These matrix vector products for the electrically large and small elements are combined, and a net delta for a combination of the matrix vector products is determined. The iteration continues until a net delta is obtained that is within the predefined limits. The matrix vector products that were last obtained are used to solve for the desired parameter. The solution for the desired parameter is then presented to a user in a tangible form; for example, on a display

Fast Multilevel Algorithms for the Electromagnetic Analysis of Quasi-Planar Structures

116 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1998.The analysis of electromagnetic scattering and radiation from quasi-planar structures is a topic of great current interest, owing to the wide range of applications. A host of structures and surfaces are included in the quasi-planar class, including rough surfaces, quantum well infrared photodetector gratings, planar microwave circuits, microstrip arrays, diffractive optical elements, and solar cells. The prediction of electromagnetic radiation and scattering is essential in applications involving the structures listed above. Possibly the most widespread class of techniques for this purpose is based on integral-equation formulations and method of moments (MoM) solutions. In such an approach, analysis problems are reduced to solutions of matrix equations of dimension N, where N is dependent on the electrical dimensions of the scatterer. Direct inversion of a large matrix can become impractical for even moderately large N, owing to a computational cost of O(N\sp{3}). Furthermore, even the O(N\sp{2}) CPU time (per iteration) and memory requirements of iterative solvers can become prohibitive for frequently encountered, large-scale, realistic problems. In this dissertation, new multilevel, rigorous, integral-equation solution techniques, based on a steepest-descent fast multipole (SDFMM) formulation, are developed for solving scattering problems involving large quasi-planar structures. These techniques promise to open the door to the full-wave analysis of complex quasi-planar structures to an extent not possible to date, owing to their O(N) CPU time (per iteration) and memory requirements. The SDFMM relies on a combined steepest-descent path and an inhomogeneous plane-wave representation of Greens' functions, and exploits the quasi-planarity of scatterers to reduce the computational complexity. In this dissertation, the SDFMM is developed in its full generality to tackle a host of electromagnetic scattering problems that find application in remote sensing, microelectronic devices, and communication systems. Large and flexible computer codes are written for analyzing scattering from perfectly conducting and penetrable rough surfaces, for studying optical absorption by quasi-random gratings in quantum-well infrared photodetectors, and for predicting radiation and scattering from large and finite microstrip antenna arrays.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

Rapid analysis of perfectly conducting and penetrable quasi-planar structures with the steepest descent fast multipole method

The applicability of the steepest descent fast multipole method (SDFMM) to the analysis of scattering and radiation from a large class of quasi-planar structures, including rough surfaces, gratings, and microstrip antennas, is demonstrated in this paper. The SDFMM was first devised for the fast solution of scattering from perfectly conducting rough surfaces. Here, the technique is extended and applied to the analysis of scattering and radiation from arbitrarily shaped, multi-region penetrable and perfectly conducting quasi-planar structures. This technique promises to open the door to accurate full-wave electromagnetic analysis of much larger and more complex problems than is possible with prevailing techniques.link_to_subscribed_fulltex

Combined steepest descent-fast multipole algorithm for the analysis of three-dimensional scattering by rough surfaces

The three-dimensional scattering by rough surfaces is analyzed using a combined steepest descent-fast multipole method algorithm (SDFMM) technique. The feature of this approach are: advantage is taken of the fact that a rough surface is nearly planar to derive efficient numerical integration rules for the Sommerfield integral representation of the free space Green's function; the Hankel functions arising in such an integration are evaluated using a Fast Multiple Method (FMM)-like algorithm that is tailored towards rough surfaces; and the proposed algorithm has O(N) CPU time and storage requirements. The technique is numerically rigorous and its accuracy can be controlled as desired.link_to_subscribed_fulltex

SDFMM-based fast analysis of radiation and scattering from finite microstrip structures

Steepest descent fast multipole method (SDFMM) is applied to the full-wave analysis of microstrip structures on finite substrates and ground planes. The quasi-planar nature of such structures is exploited to obtain matrix-vector products in O(N) CPU time and memory, resulting on dramatic solution efficiency. The required identification of independent basis functions, Nind in number, and enforcement of appropriate boundary conditions are incorporated through another matrix transformation. SDFMM permits the solution of scattering and radiation from extremely large and complex structures within realistic times.link_to_subscribed_fulltex

Moore meets maxwell

Moore's Law has driven the semiconductor revolution enabling over four decades of scaling in frequency, size, complexity, and power. However, the limits of physics are preventing further scaling of speed, forcing a paradigm shift towards multicore computing and parallelization. In effect, the system is taking over the role that the single CPU was playing: high-speed signals running through chips but also packages and boards connect ever more complex systems. High-speed signals making their way through the entire system cause new challenges in the design of computing hardware. Inductance, phase shifts and velocity of light effects, material resonances, and wave behavior become not only prevalent but need to be calculated accurately and rapidly to enable short design cycle times. In essence, to continue scaling with Moore's Law requires the incorporation of Maxwell's equations in the design process. Incorporating Maxwell's equations into the design flow is only possible through the combined power that new algorithms, parallelization and high-speed computing provide. At the same time, incorporation of Maxwell-based models into circuit and system-level simulation presents a massive accuracy, passivity, and scalability challenge. In this tutorial, we navigate through the often confusing terminology and concepts behind field solvers, show how advances in field solvers enable integration into EDA flows, present novel methods for model generation and passivity assurance in large systems, and demonstrate the power of cloud computing in enabling the next generation of scalable Maxwell solvers and the next generation of Moore's Law scaling of systems. We intend to show the truly symbiotic growing relationship between Maxwell and Moore