Dear Sjoerd, I am still struggling with this code, not working the way it should, for 4 core computer. I tried many things in between, but nothing seems to be working.

Will appreciate if you can spare some time and have a piece of advice on this. Thanks

By the looks of it, your code can be optimized quite a bit. It's a bit to much to go through everything, but I really recommend you avoid using For loops in Mathematica since it's rather inefficient and there simply are better tools to use. Here are some references on good and efficient Mathematica programming practices:

• https://mathematica.stackexchange.com/questions/134609/why-should-i-avoid-the-for-loop-in-mathematica

• https://mathematica.stackexchange.com/questions/18/where-can-i-find-examples-of-good-mathematica-programming-practice

• https://mathematica.stackexchange.com/questions/18393/what-are-the-most-common-pitfalls-awaiting-new-users

Now as for why your code doesn't work well in parallel: I'm going to hazard a guess and say that one of the problems is your use of the capital K as a variable. Mathematica uses this symbol (like many other capitals, such as N, C and D), which you can tell by the fact that it turns black when you type it in a notebook (unlike other symbols, which start blue and only turn black when you give them a value). I'm guessing that updating K causes the subkernels to talk to each other, though I might be wrong. However, your code is difficult to read and there may be numerous other inefficiencies and problems that I can't find without really taking it apart.

Without any further details, all I can say is: please make sure that your operation gets parallelized correctly. There are many reasons why parallelization can fail to be efficient. A very common cause is the sharing of values between sub kernels: the moment the kernels need to start talking to each other (or the master kernel) performance often goes down dramatically. Please make sure that each task that gets send to the sub kernels is independent of the other ones for the best performance.

Another common reason is simply failing to distribute the correct definitions to the sub kernels. If that happens, there is effectively no parallelization whatsoever since the kernels return the assignment unfinished and leave it to the master kernel to actually evaluate everything.