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Foil 33 Essential Structure of Message Parallel O(N2) Algorithm - I

From Fox Presentation Fall 1995 CPS615 Basic Simulation Track for Computational Science -- Fall Semester 97. by Geoffrey C. Fox


Let MPGrav(i) return the acceleration of i'th particle which is specified by position X(i) and velocity V(i)
The kernel of algorithm increments X(i),V(i) from t to t+h using Runge-Kutta method.
This involves 4 function calls to MPGrav(i) for the four different choices of position and time needed in the Runge-Kutta method.
Let Xuse(i) be position vector used in each function call. Then we have
(time,Xuse) = (t,X) (t+h/2, X + (h/2)Dxa) (t+h/2, X + (h/2)Dxb) (t+h, X + hDxc)
where Dxa Dxb Dxc are shift vectors calculated by previous phase of Runge-Kutta method



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