Thanks Alex, I got your email, I will check out the document. Thanks and Cheers! - vihan On 1 October 2015 at 05:38, Alex Patriciu wrote:

Hi Vihan,

I built a GPU implementation of two parallel ODE solvers a Adams-Bashforth-Moulton with 4 steps memory and a 4th order Runge-Kutta for some linear systems simulator a couple of years ago. The parallelization technique is not new as it is a prefix sum application (Guy E. Blelloch, Prefix Sums and Their Applications). The implementation was using internally some boost libraries; outwards interfaces for plain C, Python, and Matlab were implemented. I will send you the documentation and link to my git sources if interested on your personal email. There is no point in spamming the boost list with "non boost" items.

Some thoughts 1. It will be hard to have an interface compatible with odeint for a parallel ode solver. If you want to use a stepper approach, then you will be able to parallelize only the operations in one step ( Matrix - Vector multiplications and SAXPY operations). This will not give you enough GPU load for small systems. Therefore, for 12-15 variables I do not think that you will get any advantage using the GPU versus the CPU. 2. One way to achieve good GPU load (and performance) is to use a Prefix Sum to parallelize operations for several simulation times simultaneously. This is doable and the theory is relatively straight forward but it usually leads to an increased number of operations. However, adaptive time stepping will not be easy to implement.

Best, Alex

On Mon, Sep 28, 2015 at 1:32 AM, Vihan Pandey wrote:

...

Dear all,

I am trying to integrate a simple 2 variable ODE system. I wanted to know which of the solvers listed here :

http://www.boost.org/doc/libs/1_56_0/libs/numeric/odeint/doc/html/boost_nume...

are parallelised for multicore CPU’s and GPU’s? Perhaps using Thrust for the Nvidia/CUDA GPU end of things?

I am principally interested if someone has managed to make/port a library for parallelised RK45 methods. Please note in later work I plan on having more ODE's - probably systems of 12-15 parameters though they will be all be first order equations.

Thanks and Cheers!

- vihan

-- Listening to Ozzy again!

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-- ``Skepticism is healthy only to a limited extent. Being skeptical about proofs and programs (particularly your own) will probably keep your grades healthy and your job fairly secure. But applying that much skepticism will probably also keep you shut away working all the time, instead of letting you get out for exercise and relaxation. Too much skepticism is an open invitation to the state of rigor mortis, where you become so worried about being correct and rigorous that you never get anything finished. -A skeptic" Taken from Concrete Mathematics by Graham, Knuth, and Patashnik

Hi Mario, Thanks for the reply, I will check the links out. Thanks and Cheers! - vihan On 1 October 2015 at 14:49, Mario Mulansky wrote:

Hi vihan,

On Monday, September 28, 2015 11:02:21 AM Vihan Pandey wrote:

...

Dear all,

I am trying to integrate a simple 2 variable ODE system. I wanted to know which of the solvers listed here :

http://www.boost.org/doc/libs/1_56_0/libs/numeric/odeint/doc/html/boost_nume

...

ric_odeint/getting_started/overview.html

are parallelised for multicore CPU’s and GPU’s? Perhaps using Thrust for the Nvidia/CUDA GPU end of things?

odeint provides parallelization backends for explicit steppers (RK methods) based on CUDA (via thrust) [1], OpenCL [2] and OpenMP/MPI [3].

...

I am principally interested if someone has managed to make/port a library for parallelised RK45 methods. Please note in later work I plan on having more ODE's - probably systems of 12-15 parameters though they will be all be first order equations.

In my experience, parallelization only makes sense if you have at least ~100 variables for CPUs, and at least ~100000 for GPUs. For smaller problems you might be able to get some performance improvements by using SIMD [4,5].

Best, Mario

[1]

http://www.boost.org/doc/libs/1_56_0/libs/numeric/odeint/doc/html/boost_nume... [2]

http://www.boost.org/doc/libs/1_56_0/libs/numeric/odeint/doc/html/boost_nume... [3]

http://www.boost.org/doc/libs/1_56_0/libs/numeric/odeint/doc/html/boost_nume... [4] http://www.codeproject.com/Articles/841136/Boosting-ODE-simulations-with-Boo... [5] http://www.italiancpp.org/dettagli-meetup-firenze-2015/#cpu-power

...

Thanks and Cheers!

- vihan

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-- ``Skepticism is healthy only to a limited extent. Being skeptical about proofs and programs (particularly your own) will probably keep your grades healthy and your job fairly secure. But applying that much skepticism will probably also keep you shut away working all the time, instead of letting you get out for exercise and relaxation. Too much skepticism is an open invitation to the state of rigor mortis, where you become so worried about being correct and rigorous that you never get anything finished. -A skeptic" Taken from Concrete Mathematics by Graham, Knuth, and Patashnik