STEP ONE OF TWO:First of all the mesh is used as an analyzing device in fluid dynamics that the fluid arbitrarily absorbing and emitting photons (hence the name radiation hydrodynamics)passes through the mesh, and the ALE stands for Arbitrary Lagrangian Eulerian moving mesh...As the step in time (time step) continues, the mesh becomes more and more distorted, thus becoming an asymptotic algorithm When the time step runs out, the mesh must be given up and thus from the collapsed mesh we get a polynomal...a function f that will give us the ratio of its position to time at any given point in space, thus recreating a mesh with the delta derived from the function...The mesh can continue to another time step. using the method known as the Monte Carlo method, we view the system from the outside until the time step runs out, then we can integrate another systems time to activate the Eulerian codes that are simplified units of information that can be combined to create the mesh. Part two...Umm..Pending...