Solution of electromagnetic scattering problems involving curved surfaces

Ankara : Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 1997.Thesis (Master's) -- Bilkent University, 1997.Includes bibliographical references leaves 123-126.The method of moments (MoM) is an efficient technique for the solution of electromagnetic scattering problems. Problems encountered in real-life applications are often three dimensional and involve electrically large scatterers with complicated geometries. When the MoM is employed for the solution of these problems, the size of the resulting matrix equation is usually large. It is possible to reduce the size of the system of equations by improving the geometry modeling technique in the MoM algorithm. Another way of improving the efficiency of the MoM is the fast multipole method (FMM). The FMM reduces the computational complexity of the convensional MoM. The FMM has also lower memory-requirement complexity than the MoM. This facilitates the solution of larger problems on a given hardware in a shorter period of time. The combination of the FMM and the higher-order geometry modeling techniques is proposed for the efficient solution of large electromagnetic scattering problems involving three-dimensional, arbitrarily shaped, conducting suriace scatterers.Sertel, KubilayM.S

Method of moments solution of volume integral equations using parametric geometry modeling

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94709/1/rds4692.pd

Fast integral methods for conformal antenna and array modeling in conjunction with hybrid finite element formulations

Fast integral methods are used to improve the efficiency of hybrid finite element formulations for conformal antenna and array modeling. We consider here cavity-backed configurations recessed in planar and curved ground planes as well as infinite periodic structures with boundary integral (BI) terminations on the top and bottom bounding surfaces. Volume tessellation is based on triangular prismatic elements which are well suited for layered structures and still give the required modeling flexibility for irregular antenna and array elements. For planar BI terminations of finite and infinite arrays the adaptive integral method is used to achieve O(NlogN) computational complexity in evaluating the matrix-vector products within the iterative solver. In the case of curved mesh truncations for finite arrays the fast multipole method is applied to obtain O(N1.5) complexity for the evaluation of the matrix-vector products. Advantages and disadvantages of these methods as they relate to different applications are discussed, and numerical results are provided

Quantitative comparison of rooftop and RWG basis functions

The `rooftops' (RT) basis functions (BFs) are well suited for the modeling of geometries that conform to Cartesian coordinates, whereas the Rao, Wilton, and Glisson subdomains (RWG) BFs are capable of modeling flat-faceted approximations of arbitrary geometries. Both basis functions can also be used in modeling unknown functions transformed from the real space to the parametric space of a curved surface. The RT and RWG basis functions have many common features: they are defined on tow neighboring subdomains and the unknown is associated with the common edge between these two subdomains; thus they are edge functions. The two BFs also differ in the way they define the direction of the current

Hybrid finite element modelling of conformal antenna and array structures utilizing fast integral methods

Hybrid finite element methods (FEM) which combine the finite element and boundary integral methods have been found very successful for the analysis of conformal finite and periodic arrays embedded on planar or curved platforms. A key advantage of these hybrid methods is their capability to model inhomogeneous and layered material without a need to introduce complicated Green's functions. Also, they offer full geometrical adaptability and are thus of interest in general-purpose analysis and design. For the proposed hybrid FEM, the boundary integral is only used on the aperture to enforce the radiation condition by employing the standard free space Green's function. The boundary integral truncation of the FEM volume domain, although necessary for rigor, is also the cause of substantial increase in CPU complexity. In this paper, we concentrate on fast integral methods for speeding-up the computation of these boundary integrals during the execution of the iterative solver. We consider both the adaptive integral method (AIM) and the fast multipole method (FMM) to reduce the complexity of boundary integral computation down to []( N α ) with α <1.5. CPU and memory estimates are given when the AIM and FMM accelerations are employed as compared to the standard []( N 2 ) algorithms. In addition, several examples are included to demonstrate the practicality and application of these fast hybrid methods to planar finite and infinite arrays, frequency selective surfaces, and arrays on curved platforms. Copyright © 2000 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/35033/1/347_ftp.pd

Method of moments solution of volume integral equations using parametric geometry modeling

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94709/1/rds4692.pd

Multilevel fast multipole method for modeling permeable structures using conformal finite elements.

The analysis of penetrable structures has traditionally been carried out using partial differential equation methods due to the large computation time and memory requirements of integral equation methods. To reduce this computational bottle neck, this thesis focuses on fast integral equation methods for modeling penetrable geometries with both dielectric and magnetic material properties. Previous works have employed the multilevel fast multipole method for impenetrable targets in the context of flat-triangular geometry approximations. In this thesis, we integrate the multilevel fast multipole method with surface and volume integral equation techniques to accurately analyze arbitrarily curved inhomogeneous targets. It is demonstrated that conformal geometry modeling using curvilinear elements achieve higher accuracy at lower sampling rates. Also, the combined use of curvilinear elements and the multilevel fast multipole method allows for significantly faster and more efficient numerical methods. The proposed method reduces the traditional O( N2) computational cost down to O( N log N) and thus practical size geometries can be analyzed. Several example calculations are given in the thesis along with comparisons with partial differential equation methods.Ph.D.Applied SciencesElectrical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/123472/2/3079526.pd

Comparison of surface-modeling techniques

Solution techniques based on surface integral equations are widely used in computational electromagnetics. The accurate surface models increase the accuracy solutions by using exact and flat-triangulation models for a sphere. For a required solution accuracy, the problem size is significantly reduced by using geometry models for the scatterers. The dependence of the accuracy of the solution on the geometry modeling is investigated

Users Manual for FMM-SWITCH

http://deepblue.lib.umich.edu/bitstream/2027.42/21518/2/rl2495.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/21518/1/rl2495.0001.001.tx