Efficient algorithms for the analysis of large-scale electromagnetic problems on Beowulf parallel computing platform

Abstract

The purpose of this research work is to study efficient computational methods in solving electromagnetic problems. It is no doubt that the most difficult parts are long computation time and rigorous memory requirement. In order to tackle these problems, parallel computation technique is presented in this thesis. Though nowadays increase of the CPU speed and memory capability, the cost of personal computer (PC) is nevertheless reduced significantly. We can appreciate the cost-effectiveness of the Beowulf cluster, which is perhaps the easiest parallel computing platform that one can build by oneself. By using the Message-Passing Interface (MPI), PCs communication is utilized in our computation. Applications with fast algorithms will be illustrated. Firstly, parallel FDTD algorithm, demonstrated with active integrated antenna array (AIA), is used to reduce the computational requirements. A four-unit array with dual modes and dual frequencies is presented. The electronic circuit has been analyzed using a tightly coupled combination of FDTD with circuit simulator SPICE (FDTD-SPICE). The FDTD modeling allows direct access on all SPICE device models. Two typical amplifier circuits will be presented as examples. Another fast algorithm is then presented for solving the electric field time-domain integral equation pertinent to the analysis of surface scattering phenomena. The proposed time-domain sparse matrix/canonical grid (TDSM/CG) method permits to enhance the classical marching-on-in-time (MOT) scheme. The computational cost of analyzing surface scattering phenomena using TDSM/CG+MOT schemes scales as 0(N Log N) as opposed to 0(N2) for classical MOT methods, where N is the numbers of spatial basis functions discretizing the current induced on the scatterer. Numerical results that demonstrate the efficacy of the proposed solver in analyzing transient scattering form electrically large structures and that confirm the above complexity estimations are presented. Apart from TDSM/CG, the SM/CG on microstrip reflectarray will be discussed. Normally, we may employ many sub-domain basis functions to model the surface currents, which are induced on each of the radiating elements. Therefore, rigorous numerical analysis of microstrip reflectarrays always requires to solve a large matrix equation arises from the unknown currents on over one thousand elements. With all mutual-coupling included, we need to look for full-matrix solutions with tens of thousand unknowns. As a result, the construction of matrix elements requires substantial amount of inestimable computational time. To address these problems, the SM/CG method, which has a computational complexity of O(N log N), is implemented in the parallel computing platform. Fast Fourier Transforms (FFTs) is used to compute the iterative solution in the Method of Moments (MoM) matrix expansions. It is found that this method improves the matrix fill time and solution time, efficiently. The SM/CG technique definitely saves a lot of memory requirement and computing time. However, it may not converge or involve long iteration for the reason of fine gird size allocations. Therefore, improvement by using Characteristic Basis Functions (CBF) will then be made. By applying full-matrix inversion scheme via the use of CBFs derived for each array element, the number of unknowns substantially reduced. The CBFs are constructed using Foldy-Lax equations in which all the multiple-scattering effects are efficiently accounted for using the SM/CG method. Three different reflectarrays, comprised of 1,117 dipole, square patch and spiral elements, are analyzed. By extending the use of CBF, the electromagnetic scattering from a dense medium consisting of dielectric scatterers such as densely packed and electrically small dielectric scatterers will be presented. The MoM will be applied to solve the volumetric integral equations of the electric fields. In the discussion of CBF approach, four strategies, namely General, XYZ, Cluster and Cluster-XYZ schemes, will be compared. Numerical results illustrate rigorous simulation of dense medium scattering problem, having thousands of dielectric scatterers and more than 500,000 unknowns, are obtained.

Date of Award	16 Jul 2007
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Chi Hou CHAN (Supervisor)