ITERATIVE SOLUTION OF MULTIPLE RIGHT HAND SIDE MATRIX EQUATIONS FOR FREQUENCY DOMAIN MONOSTATIC RADAR CROSS SECTION CALCULATIONS

Abstract

Monostatic rcs characterisation using integral equation methods in the frequency domain requires the solution of very large matrix equations with multiple right hand sides. Although costly for a single right hand side, direct methods are attractive in that subsequent right hand sides are very cheap. Iterative methods are much cheaper for a single right hand side, but if the whole solution must be repeated for each, they become much more expensive. We investigate here the performance of a simple modification to the GCR algorithm, which allows solutions for an essentially unlimited number of right hand sides to be obtained for a modest multiple of the cost of the first. For the cases investigated, with up to 360 right hand sides on bodies up to 15 wavelengths long, with matrices up to 20,440 by 20,440 in size, this multiple was below ~10. Costs seem to rise with the number of right hand sides till the surface field is in some sense characterised, and thereafter subsequent illumination angles are essentially free. An investigation of cost scaling on a set of spheres, ranging from ~1 to 7 wavelengths in diameter, seems to indicate the cost of full monostatic characterisation to scale with about the fifth power of frequency