Many-body effects and matrix inversion in low-Reynolds-number hydrodynamics

It is shown that the method of reflections in resistance form (with truncated multipoles) is one of many possible iterative methods to obtain the inverse of the mobility matrix (with the same truncation) in low-Reynolds-number hydrodynamics. Although the method of reflections in the mobility form is guaranteed to converge, it is found that in the resistance form the method may fail to converge. This breakdown is overcome by conjugate-gradient-type iterative methods, and the implications of the iterative method for low-Reynolds-number hydrodynamics are discussed.