A Novel Broadband Multilevel Fast Multipole Algorithm With Incomplete-Leaf Tree Structures for Multiscale Electromagnetic Problems

An efficient and versatile broadband multilevel fast multipole algorithm (MLFMA), which is capable of handling large multiscale electromagnetic problems with a wide dynamic range of mesh sizes, is presented. By invoking a novel concept of incomplete-leaf tree structures, where only the overcrowded boxes are divided into smaller ones for a given population threshold, versatility of using variable-sized boxes is achieved. Consequently, for geometries containing highly overmeshed local regions, the proposed method is always more efficient than the conventional MLFMA for the same accuracy, while it is always more accurate if the efficiency is comparable. Furthermore, in such a population-based clustering scenario, the error is controllable regardless of the number of levels. Several canonical examples are provided to demonstrate the superior efficiency and accuracy of the proposed algorithm in comparison with the conventional MLFMA

Geniş bantlı çok-seviyeli hızlı çokkutup yönteminin çok-ölçekli elektromanyetik problemler için gerçekleştirilmesi

Cataloged from PDF version of article.Thesis (Ph.D.): Bilkent University, Department of Electrical and Electronics Engineering, İhsan Doğramacı Bilkent University, 2016.Includes bibliographical references (leaves 185-194).Fast multipole method (FMM) in computational physics and its multilevel version, i.e., multilevel fast multipole algorithm (MLFMA) in computational electromagnetics are among the best known methods to solve integral equations (IEs) in the frequency-domain. MLFMA is well-accepted in the computational electromagnetic (CEM) society since it provides a full-wave solution regarding Helmholtz-type electromagnetics problems. This is done by discretizing proper integral equations based on a predetermined formulation and solving them numerically with O(N logN) complexity, where N is the number of unknowns. In this dissertation, we present two broadband and efficient methods in the context of MLFMA, one for surface integral equations (SIEs) and another for volume integral equations (VIEs), both of which are capable of handling large multiscale electromagnetics problems with a wide dynamic range of mesh sizes. By invoking a novel concept of incomplete-leaf tree structures, where only the overcrowded boxes are divided into smaller ones for a given population threshold, a versatile method for both types of IEs has been achieved. Regarding SIEs, for geometries containing highly overmeshed local regions, the proposed method is always more efficient than the conventional MLFMA for the same accuracy, while it is always more accurate if the efficiency is comparable. Regarding VIEs, for inhomogeneous dielectric objects possessing variable mesh sizes due to different electrical properties, in addition to obtaining similar results from the proposed method, a reduction in the storage is also achieved. Several canonical and also real-life examples are provided to demonstrate the superior efficiency and accuracy of the proposed algorithm in comparison to the conventional MLFMA.by Manouchehr Takrimi.Ph.D

Incomplete-Leaf Multilevel Fast Multipole Algorithm for Multiscale Penetrable Objects Formulated With Volume Integral Equations

Recently introduced incomplete-leaf (IL) tree structures for multilevel fast multipole algorithm (referred to as IL-MLFMA) is proposed for the analysis of multiscale inhomogeneous penetrable objects, in which there are multiple orders of magnitude differences among the mesh sizes. Considering a maximum Schaubert-Wilton-Glisson function population threshold per box, only overcrowded boxes are recursively divided into proper smaller boxes, leading to IL tree structures consisting of variable box sizes. Such an approach: 1) significantly reduces the CPU time for near-field calculations regarding overcrowded boxes, resulting a superior efficiency in comparison with the conventional MLFMA where fixed-size boxes are used and 2) effectively reduces the computational error of the conventional MLFMA for multiscale problems, where the protrusion of the basis/testing functions from their respective boxes dramatically impairs the validity of the addition theorem. Moreover, because IL-MLFMA is able to use deep levels safely and without compromising the accuracy, the memory consumption is significantly reduced compared with that of the conventional MLFMA. Several examples are provided to assess the accuracy and the efficiency of IL-MLFMA for multiscale penetrable objects

Solution of Potential Integral Equations with NSPWMLFMA

In this contribution, we present a numerical implementation of recently developed potential integral equations (PIEs) by using nondirective stable plane wave multilevel fast multipole algorithm (NSPWMLFMA). The proposed method is efficient and accurate to solve large scattering problems involving perfectly conducting bodies with geometrical details, which require dense discretizations with respect to the operating wavelength. Numerical results in the form of scattered field from various objects are provided to assess the accuracy and efficiency of PIEs solved using NSPWMLFMA

Broadband Analysis of Multiscale Electromagnetic Problems: Novel Incomplete-Leaf MLFMA for Potential Integral Equations

Recently introduced incomplete tree structures for the magnetic-field integral equation are modified and used in conjunction with the mixed-form multilevel fast multipole algorithm (MLFMA) to employ a novel broadband incomplete-leaf MLFMA (IL-MLFMA) to the solution of potential integral equations (PIEs) for scattering/radiation from multiscale open and closed surfaces. This population-based algorithm deploys a nonuniform clustering that enables to use deep levels safely and, when necessary, without compromising the accuracy resulting in an improved efficiency and a significant reduction for the memory requirements (order of magnitudes), while the error is controllable. The superiority of the algorithm is demonstrated in several canonical and real-life multiscale geometries

Broadband Multilevel Fast Multipole Algorithm For Large-Scale Problems With Nonuniform Discretizations

We present a broadband implementation of the multilevel fast multipole algorithm (MLFMA) for fast and accurate solutions of multiscale problems involving highly nonuniform discretizations. Incomplete tree structures, which are based on population-based clustering with flexible leaf-level boxes at different levels, are used to handle extremely varying triangulation sizes on the same structures. Superior efficiency and accuracy of the developed implementation, in comparison to the standard and broadband MLFMA solvers employing conventional tree structures, are demonstrated on practical problems