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A survey of various computer architectures for solution of large matrix equations

โœ Scribed by Madhavan Swaminathan; Tapan K. Sarkar


Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
987 KB
Volume
8
Category
Article
ISSN
0894-3370

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โœฆ Synopsis


In electromagnetics, a numerical technique that finds immense application is the method of moments. This method reduces the boundary value problem containing integro-differential equations into the form A X = Y , where A is a full complex matrix, that is known and X is the unknown to be solved for the given excitation Y . In this paper, the matrix equation has been solved on various computers such as the VAX 3500, VAX 8530, Multimax 320, Alliant FX/80 and IBM 3090-600E. Two of the established methods, viz. gaussian elimination and the conjugate gradient method have been used to solve the above matrix equations. A detailed timing analysis has been done to bring out the features of various computer architectures.

Any approach that deals with electromagnetic scattering and radiation in the frequency domain from arbitrarily shaped conducting structures should place special emphasis on three specific areas:

( 1) Development of the algorithm for treating structures with arbitrary geometries. This includes (2) Development of an efficient procedure for matrix generation and solution.

(3) Use of vector and parallel computation as an added tool for solution speed-up.

In this paper, emphasis will be put on item (3). The electric field integral equation (EFIE) in the frequency domain will be made use of here, because of its ability to account for scattering from structures having vanishing thickness. This is an essential feature, necessary in the area of microstrips owing to the infinitesimal thickness of the bodies involved. The method of moments objects that are either open or closed.


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## Abstract In this paper, we introduce a novel approach for an efficient solution of matrix equations arising in the method of moments (MoM) formulation of electromagnetic scattering problems. This approach is based on the characteristic basis functions (CBFs), which are used to substantially redu