Bi-Conjugate Gradient Algorithm for Solution of Integral Equations Arising in Electromagnetic Scattering Problems

Abstract : The bi-conjugate gradient (bi-CG) algorithm is applied to numerically solve linear equation systems resulting from integral equations arising in electromagnetic scattering problems. The basic advantage of using this algorithm over traditional methods, such as matrix inversion, is that the algorithm is iterative in nature. The iterative nature allows the user to control the residual error in the final solution. Also, the algorithm can be implemented without storing the coefficient matrix, thus providing huge saving in storage requirements. It was realized that the existing code that utilized matrix inversion to solve the linear equation system was limited to a coarse discretization of the geometry. This code could not handle very fine geometry discretization due to storage limitations. With the implementation of the bi-CG algorithm, this limitation was overcome. The present code can very easily handle very finw discretizations, thereby vastly improving the utility of the computer code. This report outlines the bi-CG algorithm and provides its implementation to solve an electromagnetic scattering problem of a nanowire illuminated by a plane wave. The report also includes a complete FORTRAN listing of the code.