Many specific methods to improve both the efficiency and the accuracy of the numerical solution of periodic problems have been proposed, with reference to several configurations of sources in various environments (e.g., free space, multilayered media). Integral equations can be formulated by including the proper periodicity in their kernel, thus defining periodic Green's functions, usually expressed through impractical slowly-converging series. Effective algorithms for their calculation, known as "acceleration techniques," are then required for their fast computation. Many approaches have been proposed in the free-space case [1]; one of the most effective methods has been proven to be the Ewald decomposition, with various formulations according to the kind of periodicity analyzed [2]. Fewer results are available to treat periodic inclusions in generally layered media, where dyadic Green's functions are necessary, due to the stratification of the medium. In order to allow for the analysis of arbitrarily shaped inclusions, a spatial-domain method of moments should be adopted. In this case, a mixed-potential approach (according to formulation C in [3]) leads to a reduced spatial singularity. Some techniques have previously been proposed in the literature with reference to planar problems, where the unknown currents are orthogonal to the directions of stratification. In this case, a reduced number of potentials are involved, and their acceleration can be let with the same methods used in free-space problems [4]. If vertical currents are also present, as in the case of arbitrary-shaped inclusions, other components of the Green's dyads are required: in [5] some basic information was given about a new approach to accelerate these vertical components due to line sources periodic along one direction. In this work, the method of analysis is recalled and new results on canonical periodic structures are presented, yielding very good agreement with results from a finite-element commercial code. © 2010 IEEE.
Accelerated Solution of Periodic Problems Involving Arbitrarily-Shaped Cylindrical Inclusions in Stratified Media / G., Valerio; D. R., Wilton; D. R., Jackson; Galli, Alessandro. - (2010), pp. 1-4. (Intervento presentato al convegno 2010 IEEE International Symposium Antennas and Propagation/CNC-USNC/URSI Radio Science Meeting tenutosi a Toronto, ON nel JUL 11-17, 2010) [10.1109/aps.2010.5561123].
Accelerated Solution of Periodic Problems Involving Arbitrarily-Shaped Cylindrical Inclusions in Stratified Media
GALLI, Alessandro
2010
Abstract
Many specific methods to improve both the efficiency and the accuracy of the numerical solution of periodic problems have been proposed, with reference to several configurations of sources in various environments (e.g., free space, multilayered media). Integral equations can be formulated by including the proper periodicity in their kernel, thus defining periodic Green's functions, usually expressed through impractical slowly-converging series. Effective algorithms for their calculation, known as "acceleration techniques," are then required for their fast computation. Many approaches have been proposed in the free-space case [1]; one of the most effective methods has been proven to be the Ewald decomposition, with various formulations according to the kind of periodicity analyzed [2]. Fewer results are available to treat periodic inclusions in generally layered media, where dyadic Green's functions are necessary, due to the stratification of the medium. In order to allow for the analysis of arbitrarily shaped inclusions, a spatial-domain method of moments should be adopted. In this case, a mixed-potential approach (according to formulation C in [3]) leads to a reduced spatial singularity. Some techniques have previously been proposed in the literature with reference to planar problems, where the unknown currents are orthogonal to the directions of stratification. In this case, a reduced number of potentials are involved, and their acceleration can be let with the same methods used in free-space problems [4]. If vertical currents are also present, as in the case of arbitrary-shaped inclusions, other components of the Green's dyads are required: in [5] some basic information was given about a new approach to accelerate these vertical components due to line sources periodic along one direction. In this work, the method of analysis is recalled and new results on canonical periodic structures are presented, yielding very good agreement with results from a finite-element commercial code. © 2010 IEEE.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
