Paired Pulse Basis Functions for the Method of Moments EFIE Solution of Electromagnetic Problems Involving Arbitrarily-shaped, Three-dimensional Dielectric Scatterers

A pair of basis functions is presented for the surface integral, method of moment solution of scattering by arbitrarily-shaped, three-dimensional dielectric bodies. Equivalent surface currents are represented by orthogonal unit pulse vectors in conjunction with triangular patch modeling. The electric field integral equation is employed with closed geometries for dielectric bodies; the method may also be applied to conductors. Radar cross section results are shown for dielectric bodies having canonical spherical, cylindrical, and cubic shapes. Pulse basis function results are compared to results by other methods

An Alternate Set of Basis Functions for the Electromagnetic Solution of Arbitrarily-Shaped, Three-Dimensional, Closed, Conducting Bodies Using Method of Moments

In this work, we present an alternate set of basis functions, each defined over a pair of planar triangular patches, for the method of moments solution of electromagnetic scattering and radiation problems associated with arbitrarily-shaped, closed, conducting surfaces. The present basis functions are point-wise orthogonal to the pulse basis functions previously defined. The prime motivation to develop the present set of basis functions is to utilize them for the electromagnetic solution of dielectric bodies using a surface integral equation formulation which involves both electric and magnetic cur- rents. However, in the present work, only the conducting body solution is presented and compared with other data

The Application of the Conjugate Gradient Method to the Solution of Transient Electromagnetic Scattering from Thin Wires

Previous approaches to the problem of computing scattering by conducting bodies have utilized the well-known marching-on-in-time solution procedures. However, these procedures are very dependent on discretization techniques and sometimes lead to instabilities as the time progresses. Moreover, the accuracy of the solution cannot be verified easily, and usually there is no error estimation. In this paper we describe the conjugate gradient method for solving transient problems. For this method, the time and space discretizations are independent of one another. The method has the advantage of a direct method as the solution is obtained in a finite number of steps and also of an iterative method since the roundoff and truncation errors are limited only to the last stage of iteration. The conjugate gradient method converges for any initial guess; however, a good initial guess may significantly reduce the computation time. Also, explicit error formulas are given for the rate of convergence of this method. Hence any problem may be solved to a prespecified degree of accuracy. The procedure is stable with respect to roundoff and truncation errors and simple to apply. As an example, we apply the method of conjugate gradient to the problem of scattering from a thin conducting wire illuminated by a Gaussian pulse. The results compare well with the marching-on-in-time procedure

New Basis Functions for the Electromagnetic Solution of Arbitrarily-shaped, Three Dimensional Conducting Bodies Using Method of Moments

In this work, we present a new set of basis functions, de ned over a pair of planar triangular patches, for the solution of electromagnetic scattering and radiation problems associated with arbitrarily-shaped surfaces using the method of moments solution procedure. The basis functions are constant over the function subdomain and resemble pulse functions for one and two dimensional problems. Further, another set of basis functions, point-wise orthogonal to the first set, is also de ned over the same function space. The primary objective of developing these basis functions is to utilize them for the electromagnetic solution involving conducting, dielectric, and composite bodies. However, in the present work, only the conducting body solution is presented and compared with other data

Comparative evaluation of organic zinc supplementation as proteinate with inorganic zinc in buffalo heifers on health and immunity

Graded Murrah buffalo heifers (18) were randomly allotted to 3 dietary groups varying in source and level of Zn supplementation in concentrate mixture to study the effect of organic (O) Zn (Zn proteinate; Zn-prot) supplementation (80 or 140 ppm) compared to inorganic Zn (I) (ZnSO4) (140 ppm) on serum biochemical parameters, antioxidant status and ovarian folliculogenesis. Mineral and biochemical constituents in serum and antioxidant enzyme activities in haemolysate were measured on 90th d of experiment. Antibody titres (log2) against Brucella abortus S19 and chicken RBC antigens was measured in serum at 7, 14, 21 and 28th d post sensitization (humoral immunity) and cell mediated immunity was assessed (120 d) by in-vivo delayed type hypersensitivity (DTH) against phytohemagglutinin-P (PHA-P). After 60 days of feeding, ovarian folliculogenesis study was made daily with ultrasound scanner in all the animals for next 60 days. Highest Zn concentration in serum without affecting the retention of other minerals (Cu, Mn and Fe) was observed with 140 ppm Zn supplementation as Zn-prot and mineral concentrations was comparable between 80 ppm Zn as Zn-prot and 140 ppm Zn as ZnSO4. Alkaline phosphatase, total protein, globulin, and glucose concentrations in serum increased with organic Zn supplementation. Organic Zn lowered lipid peroxidation (140O80O>140I) activities. Antibody titres against B. abortus and chicken RBC and in vivo DTH response improved with organic Zn supplementation. Similarly, irrespective of the dose, organic Zn supplementation significantly increased the number of large follicle with greater follicular size in ovary. The study indicated that 140 ppm Zn supplementation as Zn-prot resulted in better antioxidant status, immune response and folliculogenesis in ovaries than inorganic source and the Zn supplementation could be reduced from 140 to 80 ppm as Zn-prot without any adverse effect in buffalo heifers

A Faster Method of Moments Solution to Double Layer Formulation of Acoustic Scattering

In this work, the acoustic scattering problem based oil double layer formulation is solved with a novel numerical technique using method of moment's solution. A new set of basis functions, namely, Edge based Adaptive Basis Functions (EABF) are defined in the method of moment's solution procedure. The geometry of the body is divided into triangular patches and basis functions are defined oil the edges. Since the double layer formulation involves the evaluation of the hyper-singular integral, the edge based adaptive basis functions are used to make the solution faster. The matrix equations are derived for the double layer formulation. The edge based adaptive basis functions used in this work generates a diagonal moment matrix and hence do not need any matrix inversion to be carried out. The scattering cross section of the canonical shapes is used to validate the numerical solution developed and the plots are presented

Elimination of internal resonance problem associated with acoustic scattering by three-dimensional rigid body

In this work, a simple and stable numerical method is presented, utilizing the method of moments (MoM), to eliminate the internal resonance problem associated with acoustic scattering by three-dimensional rigid body subjected to a plane wave incidence. The numerical method is based on the potential theory and combines the single layer formulation (SLF) and the double layer formulation (DLF). The scattering body is approximated by planar triangular patches. For the MoM solution of SLF and DLF, the basis functions have been defined with respect to the edges to approximate the unknown source distribution. These basis functions along with an efficient testing procedure generate accurate results at all frequencies, including the characteristic frequencies. Finally, the new solution method is validated with several representative examples

A new method to generate an almost-diagonal matrix in the boundary integral equation formulation

In this work, a new numerical procedure is developed to generate an almost-diagonal matrix for the solution of boundary integral equation formulation dealing with acoustic scattering problems. The major drawback of the traditional boundary integral equation procedure resulting in a dense system matrix is eliminated in this new procedure by grouping the basis functions into a cluster. The geometry of the structure is modeled by planar triangles and the basis functions are defined on the nodes. By doing so, one can get a benefit of a smaller size matrix to begin with. Furthermore, by grouping these node-based basis functions into a cluster, an almost-diagonal matrix is generated. Thus, the solution procedure developed in this work may be utilized for very large scattering problems since the required computer resources are very low. The solution procedure developed in this work is validated for the scattering cross section of the simple shapes with the closed form solutions wherever available and with the other numerical solution procedures