An iterative method for the boundary element solution of the exterior acoustic problem (Q1100866)

The author discusses the boundary integral formulation of the exterior Neumann problem for the Helmholtz equation due to \textit{A. J. Burton} and \textit{G. F. Miller} [Proc. Roy. Soc. London Ser. A 323, 201-210 (1971; Zbl 0235.65080)], which is uniquely solvable for all frequencies as well as a similar formulation of \textit{H. Brakhage} and \textit{P. Werner} [Arch. Math. 16, 325-329 (1965; Zbl 0132.336)], \textit{R. Leis} [Math. Z. 90, 205-211 (1965; Zbl 0132.336)] and also \textit{O. I. Panich} [Usp. Mat. Nauk 20, No.1(121), 221-226 (1965; Zbl 0143.343)] for the exterior Dirichlet problem. In this paper, the author presents an iterative procedure for the efficient solution of the full linear systems arisinof gray-scale level value homogeneity, as well as that of spatial resolution. The paper also develops two-way G-quadtree/G-octree conversion procedures based on the algorithms for the binary case. These procedures provide an integrated processing environment for hierarchically represented 2D/3D images. Our approach is demonstrated with an application to the color-coding of macroautoradiography images taken from rat brains.