Abstract: The present invention provides a method of computing the motion of solid particles suspended in a fluid comprising: preparing and storing a background flow database containing an inverse evolution matrix and a background field for a given unperturbed computational flow; inputting position and orientation of suspended solid particles; determining projector matrices based on the position and orientation of the suspended solid particles; retrieving reduced space background matrices from the background flow database containing the inverse evolution matrix and the background field for the given unperturbed computational flow; preparing perturbation matrices; and calculating velocity and angular velocity of the suspended solid particles based on the reduced space background matrices and the perturbation matrices.