【FAQ】2.2 核数的影响

乔聪颖

2.2 Influence of the number of cores
2.2 核数的影响

Parallel calculation
并行计算
With parallel calculation, the work is distributed evenly between all cores – picture 43.
通过并行计算，任务会在所有内核之间平均分配 - 图43。
If there are no rounding errors, the result of the above minimal residual algorithm coincides with non-parallel version. When the so-called preconditioners are used to speed up convergence, the structure of preconditioner will depend on number of cores and the solution will be «a little» different.
如果没有舍入误差，则上述最小残留算法的结果与非并行版本一致。当使用所谓的预调节器来加速收敛时，预调节器的结构将取决于核的数量，并且解决方案将“稍有不同”。

Influence on the result
对结果的影响

Scalar product calculation
标量乘法计算
Iterational algorithms are very sensitive to iterational parameter tau. It's calculated from vector scalar products.
迭代算法对迭代参数tau非常敏感。它是根据矢量标量积（注：点乘）计算得出的。
Let – vector length, – core numbers, each core working with vector elements from to , = 1, = . Sum of products will be calculated as:  
设 – 向量长度， – 核数，每个核与从到的向量元素一起作用， = 1， = 。乘积的总和为：

Due to differences in rounding error summation, the answer is different! The answer will be different even on one core, if we sum the item in different order.
由于舍入误差求和的差异，答案是不同的！ 如果我们以不同的顺序求和的话，则即使在一个核心上，答案也将有所不同。

Rounding error
舍入误差
Machine accuracy is maximal such that is 1. On most modern computers this is , characterising density of real numbers near 1. If we know it, we can calculate difference between two numbers at any point. For example, is equal to .
机器精度是的最大值，因此为1。在大多数现代计算机上，为，表示1附近的实数密度。如果知道它的值，就可以计算任意点上两个数的差值。 例如，等于。

Different answers

不同的答案

Solution calculation
解决方案的计算
So, for different number of cores we'll get different values of and, hence, different solutions.
对于不同的核数，我们会得到不同的值，因此，（得到）不同的解决方案。
Which of them is «most correct»? None! They are all equally correct and all are solutions.
哪一个是“最正确的”?没有！它们都是同样正确的，都是解决方案。

Reserves calculation
储量计算
Another example: reserves calculation. Let be reserves in any grid block. In this case the reserves will be
另一个例子：储量计算。 令是任何网格块中的储量。 在这种情况下，储量为

Due to differences in rounding error summation, the answer is different.
由于舍入误差总和的差异，答案是不同的。
Which reserves are «most correct»?
哪个储量是“最正确的”？

Calculating well, group, network production
计算井、井组、管网的产量
The same way renumbering of items in the sum influences the result. Remember that solution accuracy is largest in wells with wells and depends on number of cores due to preconditioner.
同样地，对总和中的项目重新编号也会影响结果。请记住，在带有射孔的井中，解决方案的精度最高，并且取决于预处理器的核心数。

What to do to get «the correct answer»?
如何获得“正确答案”？
Nothing! All these results are correct. The answer (for example, field production) is not a number, but a numeric interval – picture 44.
没有什么!所有这些结果都是正确的。答案（例如，油田产量）不是一个数字，而是一个数值区间 – 图44。
This uncertainty interval due to calculation is much smaller than the uncertainty due to initial data.
由于计算产生的不确定性比初始数据产生的不确定性小得多。

（注：云里雾里。总之，把握三点，
一、内核数量会影响计算结果，本质上还是与数据精度或者数据舍入有关；
二、所有计算结果总体上构成一个解的区间，每一个都可以视为正确解；
三、数值模拟计算所造成的不确定性远小于原始数据的不确定性。--qcy）