In general, I'm agree with Christos Tsironis, however I would like to add that if you choose between a newer processor with lower rate and higher number of cores and an older one with higher rate and lower number of cores, I would suggest you the newer one. In newer processors the pipelines are more intellectual which usually results to the faster performance on smaller frequencies even for serial code. Also, the modern compilers can automatically perform some parallelization in a serial code.

In case you are going to compute some parallel algorithms, I would suggest to consider NVidea Kepler solutions.

Dear Vinicius,

It was not clear to me if you are talking about numerical integration of integrals or of differential equations. In general, the answer to your question strongly depends on the details of your problems and on its dimension. Cuda on NVidia can gives you a good opportunity to improve the code performances with a relative low cost, but it is suitable only for particular type of problems, i.e. where simple operations are repeated thousands of times. Often you have to rewrite your code, or at least the part you need to parallelize with cuda, adapting also the logic to the NVidia structure. My first experience with CUDA was a failure and the parallel calculation was slower than the serial code. You have to account fro the GPU structure when programming. But if you do this you can have speed-up on the same computer up to 100. In mean you have 10. With MPI it is simpler to parallelize the codes, adding few instructions to the code, and can give you a good efficiency too. For cuda calculations you can give a look to these papers

https://www.researchgate.net/publication/235419403_Computing_unsteady_compressible_flows_using_Roes_flux-difference_splitting_scheme_on_GPUs?ev=prf_pub

https://www.researchgate.net/publication/259085613_GPU_and_Multi-core_based_Reaction_Ensemble_Monte_Carlo_method_for_non-ideal_thermodynamic_systems?ev=prf_pub

Article Computing unsteady compressible flows using Roe’s flux-diffe...

Article GPU and Multi-core based Reaction Ensemble Monte Carlo metho...

Hi, fellows! Thank you for your help so far, I really appeciated.

Gianpiero, I apologise for not giving you all the details on the first time. I'm actually using Matlab's ode45 to compute responses from differential equations. I've already implemented many algorithms for this kind of integration (including this one, by Drormand-Prince, which they call ode45) in Java.

As I could see, each step of integration depends strongly on the previous ones, so I think this is more likely to be serial computing. However, comparing different computers I could get to no answer at all. Have a look at the attached table which I built from my experience. I could get to no conclusion at all... The computers from my laboratory are old, but seem to be oustandingly faster than any other I've tested.

In all computers I ran exaclty the same matlab code to compare their performances.

Is there anything else you can think of? It seems to me that a lighter Operating System would be a good choice after all...

Thank you all for your contributions.

Best regards,

Vinícius

Dear Vinicius

I can understand your point. However my suggestion is to avoid the use of matlab for heavy calculation problems. At the beginning we have developed REMC algorithm (second paper) in Matlab, and the execution time was days. The serial C code needed 1 -2 hours, at list 10 times faster.

You have to evaluate if each step of your code is complex enough to be parallelized. There are different C or fortran libraries to solve ODE's.

Do you use the same version of Matlab to perform the calculation on different machines?

Usually, with C or fortran code, higher clock rate or in general new technologies really improve the speed of my code. Also in this case the compiler performances has an influence, but not so high as the machine "power".

By the way, I have heard that there is a CUDA enhanced matlab.

best regards

Gianpiero

I understand, Geanpiero. I usually use matlab because it is sometimes very handy but for heavy calculations I understand that the best Idea would be to move to another language.

I've already performed a test with the calculus of prime numbers in C and Matlab and I came o the same conclusion (probably 10 or 15 times faster).

Thank you for your helpful suggestions. I'll try to implement them.

Best regards,

Vinícius

I prefer to use Mathematica

In general, newer workstations with enough RAM to handle your problem will provide good overall performance.

Depending on the hardware, you will however see huge performance variations. They are due to the efficiency of the parallelization implementation and the level of compatbility between your hardware and software, and the speed of memory access, in the CPU and in the RAM.

I had a case with a 100% CPU time difference with the same program, similar hardware but the CPU unit (one was i7, the other Xeon). The thing is that depending on the operations performed the fastest one was not always the same !

Recent MATLAB versions have shown satisfying levels of parallelization, but of course to provide an overall acceptable performance, it cannot be perfectly optimized for a specific case.

If you are using ode45, that is a general solver provided by MATLAB, I do not see how you can optimize your hardware better than following MATLAB recommandations. By the way, the MATLAB version is missing in your performance table, which could explain some strange results.

Maybe even ode45 is not very efficient to solve your problem. The fact that it is a hands-on robust solver is very useful to compute solutions without programming effort. Generality and robustness are however opposed to the concept of specific application performance.

On current computer units each hardware configuration will have its pro's and con's, so that if you do not know what computational operations are critical for you you cannot really optimize your hardware.

Best Regards,

This thread is very old...what did you decide to do and how did it work out? I'm facing this problem now...my computations are also basically serial iterations and I don't want to waste my time on parallelzation. I have a 32GB Intel workstation and I'm thinking Linux on a *spinning* hard drive with huge swap space (so as not to wear out a SSD...as I said, they're iterations). Secondary SSD for Windows in a VM? Eventually to banish it from my life? Wish I could take advantage of AMD's Infinity Fabric/Hypertransport for data locality but the dream never seems to work out.