The macromolecular technique of calculating the dipole moment of parti
cles in a mixture, such as an artificial magnetodielectric (AMD) mater
ial, is quite general and also computer intensive. The conjugate gradi
ent (CG) method has proven to be an efficient solver for equations res
ulting from the macromolecule formulation. The conjugate gradient solv
er presented here has been applied to an electric and magnetic dipole
problem with coupling of the dipole moments. The CG method is compared
to other solvers for this application.