View source for Poisson equation, solving with DFT, scalability

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Primary author of this description: [[:Ru:Участник:Виктор Степаненко|V.M.Stepanenko]], [[:Ru:Участник:Evgeny Mortikov|E.V.Mortikov]].

= Links =

For the experiments, we used the implementation of the algorithm for solving the Poisson equation by the discrete Fourier transform.

= Locality of data and computations =
== Locality of implementation ==
=== Structure of memory access and a qualitative estimation of locality ===
=== Quantitative estimation of locality ===

= Scalability of the algorithm and its implementations =
== Scalability of the algorithm ==
== Scalability of of the algorithm implementation == 

The variable [[Glossary#Start-up parameters|start-up parameters]] of this implementation and their ranges are as follows: 

*	the number of processors is a squared integer in the range [4 : 100];
*	the domain size varies in the range [100x100x100 : 250x100x100] with the step 50x100x100.

The experiments resulted in the following range for the [[Glossary#Implementation efficiency|implementation efficiency]] of this algorithm:

*	the minimum efficiency is 0,132%;
*	the maximum efficiency is 1,34%.

The following two figures show how the [[Glossary#Performance|performance]] and efficiency of this implementation depend on the variable start-up parameters. 

[[file:Poisson perf.png|thumb|center|700px|Figure 1. Parallel implementation of the algorithm. Performance as a function of the number of processors and the domain size.]] 

[[file:Poisson eff.png|thumb|center|700px|Figure 2. Parallel implementation of the algorithm. Efficiency as a function of the number of processors and the domain size. ]]

These results are in good qualitative agreement with the estimates given in the preceding section. For instance, one can see from fig. 8 that the scalability of the algorithm improves with the growth of <math>N</math>; that is, the performance improves faster with the growing number of cores. This is consistent with the fact that <math>\alpha</math> decreases with the growth of <math>N</math>, although the dependence revealed by the expression <math>\alpha=12/(6\log_2 N+1)</math> is considerably more weak. On the whole, the scalability of the algorithm is rather weak. Suppose that the domain has the size 250х100х100. When the number of cores increases by a factor 25 (from 4 to 100), the performance of calculations increases only sixfold.

= Dynamic characteristics and efficiency of the algorithm implementation =
= Run results =

[[Category:Articles in progress]]

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