Block tri-diagonal matrix formulation for inhomogeneous penetrable scattering problems

A number of methods have been introduced for generating a good approximation of sparse or banded matrices for discretizing integral equations. A banded, block tri-diagonal matrix has been formulated by Govind, Wilton,and Glisson (1984) for bodies of revolution with concentric homogeneous shells, and solved recursively. A true block tri-diagonal matrix is generated for the solution of inhomogeneous penetrable scatterers of general shape and composition. In such a representation, the operation counts would be N/sup 7/3/ for the three dimensional case.