Operator-Splitting Methods and Applications to the Direct Numerical Simulation of Particulate Flow and to the Solution of the Elliptic Monge-Ampe`re Equation

Introduction It has been known for decades that operator-splitting methods provide efficient tools for the numerical solution of complicated problems from various areas in science and engineering. New applications appear almost daily and we know of many instances where the only available practical solution methods are of the operator-splitting type. Our goal, here, is to show that operator-splitting makes almost trivial the numerical solution of outstanding problems such as:

(i) The simulation of particulate flow when the number of particles exceeds 102.