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Foil 57 Essential Structure of Message Parallel O(N2) Algorithm - I

From Fox Presentation Fall 1995 CPS615 Basic Simulation Track for Computational Science -- Fall Semester 95/96/97. by Nancy McCracken and 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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