scholarly journals Closed-Form Expressions for Numerical Evaluation of Self-Impedance Terms Involved on Wire Antenna Analysis by the Method of Moments

Electronics ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 1316
Author(s):  
Carlos-Ivan Paez-Rueda ◽  
Arturo Fajardo ◽  
Manuel Pérez ◽  
Gabriel Perilla
Keyword(s):  
Numerical Integration ◽  
Method Of Moments ◽  
Computing Time ◽  
Basis Functions ◽  
Wire Antenna ◽  
Complex Geometries ◽  
Point Matching ◽  
Piecewise Constant ◽  
Matching Procedure ◽  
Time Required

This paper proposes new closed expressions of self-impedance using the Method of Moments with the Point Matching Procedure and piecewise constant and linear basis functions in different configurations, which allow saving computing time for the solution of wire antennas with complex geometries. The new expressions have complexity O(1) with well-defined theoretical bound errors. They were compared with an adaptive numerical integration. We obtain an accuracy between 7 and 16 digits depending on the chosen basis function and segmentation used. Besides, the computing time involved in the calculation of the self-impedance terms was evaluated and compared with the time required by the adaptative quadrature integration solution of the same problem. Expressions have a run-time bounded between 50 and 200 times faster than an adaptive numerical integration assuming full computation of all constant of the expressions.

Potential of a Spheroid with Generalized Exponential Density Distribution

2015 ◽  
Vol 24 (4) ◽  
Author(s):  
B. P. Kondratyev ◽  
E. N. Kireeva
Keyword(s):  
Density Distribution ◽  
Numerical Integration ◽  
Hypergeometric Function ◽  
Computing Time ◽  
Analytical Form ◽  
Gauss Hypergeometric Function ◽  
Exponential Density ◽  
Time Required ◽  
Internal Potential

AbstractThe internal potential of an inhomogeneous layered spheroid with a small ellipticity and general exponential density distribution is derived in an analytical form. The results are presented in the form of standard Gauss hypergeometric function and validated numerically. The computing time when using this formula is noticeably smaller than the time required by numerical integration.

scholarly journals Method of Moments Simulation of Modulated Metasurface Antennas With a Set of Orthogonal Entire-Domain Basis Functions

2019 ◽  
Vol 67 (2) ◽  
pp. 1119-1130 ◽  
Author(s):  
Modeste Bodehou ◽  
David Gonzalez-Ovejero ◽  
Christophe Craeye ◽  
Isabelle Huynen
Keyword(s):  
Method Of Moments ◽  
Basis Functions ◽  
Entire Domain

scholarly journals 2-D reconstruction of atmospheric concentration peaks from horizontal long path DOAS tomographic measurements: parametrisation and geometry within a discrete approach

2006 ◽  
Vol 6 (3) ◽  
pp. 847-861 ◽  
Author(s):  
A. Hartl ◽  
B. C. Song ◽  
I. Pundt
Keyword(s):  
Cross Sections ◽  
Measurement Errors ◽  
Concentration Field ◽  
Basis Functions ◽  
Linear Functions ◽  
Background Concentration ◽  
Atmospheric Concentration ◽  
Piecewise Constant ◽  
Reconstruction Quality ◽  
Norm Principle

Abstract. In this study, we theoretically investigate the reconstruction of 2-D cross sections through Gaussian concentration distributions, e.g. emission plumes, from long path DOAS measurements along a limited number of light paths. This is done systematically with respect to the extension of the up to four peaks and for six different measurement setups with 2-4 telescopes and 36 light paths each. We distinguish between cases with and without additional background concentrations. Our approach parametrises the unknown distribution by local piecewise constant or linear functions on a regular grid and solves the resulting discrete, linear system by a least squares minimum norm principle. We show that the linear parametrisation not only allows better representation of the distributions in terms of discretisation errors, but also better inversion of the system. We calculate area integrals of the concentration field (i.e. total emissions rates for non-vanishing perpendicular wind speed components) and show that reconstruction errors and reconstructed area integrals within the peaks for narrow distributions crucially depend on the resolution of the reconstruction grid. A recently suggested grid translation method for the piecewise constant basis functions, combining reconstructions from several shifted grids, is modified for the linear basis functions and proven to reduce overall reconstruction errors, but not the uncertainty of concentration integrals. We suggest a procedure to subtract additional background concentration fields before inversion. We find large differences in reconstruction quality between the geometries and conclude that, in general, for a constant number of light paths increasing the number of telescopes leads to better reconstruction results. It appears that geometries that give better results for negligible measurement errors and parts of the geometry that are better resolved are also less sensitive to increasing measurement errors.

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