Timing Simulations for Elliptic Pdes Run Under Washcloth

Cover Timing Simulations for Elliptic Pdes Run Under Washcloth
Timing Simulations for Elliptic Pdes Run Under Washcloth
David G Korn
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All of these systems can be solved concurrently. Synchronization is needed after each of the (N-l)**2 tridiagonal systems is solved and when changing grids. The interpolation and smoothing can be simultaneously performed at distinct points in the grid; however, the amount of computation is so small that it seems better to lump N points together and perform on. Y (N-l)**2 tasks concurrently.
Using this method as many as (N-l)**2 simultaneous processes can be used on each of the grids. Since log
...N grids are used and the time per grid is proportional to N**3///PE the time to solve this three dimensional system using (N-l)**2 PE's is proportional to N.
A computer program provided by A» Jameson [5] was parallelized and under WASHCLOTH simulation. Table 3 summarizes the results for an 8x8x8 grid. The efficiency loss is primarily due to waiting time. This should be contrasted to the matrix diagonalization code discussed in [7] where the efficiency loss is due primarily to loop initialization overhead performed by each processing element.


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