Monday, 2 August 2010

Apply CUDA to solve a 1D heat transfer problem

News - On 27th June, 2010 NVIDIA released CUDA 3.1 and on 21st July, released Parallel Nsight 1.0. The download sites for CUDA Toolkit 3.1 and NVIDIA Parallel Nsight 1.0 are here and here, respectively.

I recently wrote a small piece of code using CUDA to solve a 1D heat transfer problem. The heat transfer happens along the material whose properties are density ρ = 930 kg/m3, specific heat Cp = 1340 J/(kg K) and thermal conductivity k = 0.19 W/(m K). As shown in the figure below, the computation region is illustrated by the thick orange line; the total distance is 1.6 m. There are two boundary conditions attached: at the left end, the temperature is fixed to be 0 oC, while at the right end, a heat flux q = 10 W/m2 is imposed.

If the initial temperature for the entire region is 0 oC, I want to calculate the temperature distribution along the region after 10 seconds' heat propogation.

In the previous figure, the governing heat equation, in partial differential form, has been given. It is then discretised for the internal region, i.e. the orange line, and the right end boundary, which is redly circled, respectively. In the computation, I discretised the entire distance, 1.6 m, into 32768 elements - within CUDA, 64 blocks can be used to handle these elements. On the other hand, for the time marching iteration, the time step can be determined as

in which α is the thermal diffusivity.

The calculation results, with the help of CUDA and based on float operation, are depicted as

The temperature values for x < 1.5926 m are all zero; therefore they are neglected in the picture. In order to verify the results, the same calculation was also implemented onto CPU and even COMSOL software. The implementation on CPU gave
The interesting thing concerns us is the code efficiency. Once again, I used CUDA 3.1 on my GeForce 9800 GTX+ and a single core of the Q6600 CPU, and the time durations elapsed on the GPU and the CPU for the same calculation are 1.43 s and 5.04 s, respectively. The speedup is 3.52. This speedup value is not that attractive, but it is actually supposed to be much higher when there are much more discretised elements.

I also record the temperature development, in a transient process, of the right end boundary, at which there is heat flux injected. The 10 seconds development curve is illustrated as

I didn't find an easy way to paste source code onto the blog. If you are interested, please leave a comment and the related code can be shared in any way.

News - The source code can be found in the new post on porting this CUDA program onto Mac OS X.


  1. Hallo,
    Can you please send me this code...I am experimenting with solving PDEs with CUDA and this will really help me.
    Please send me the code at my yahoo ID:
    Thanks a lot.

  2. May I ask you to share your code?
    My email address is
    Thank you

  3. Hi, thanks for the post. I'd also be interested in the code. Can you perhaps paste it here: ?


  4. Hi Manos and all,

    Thanks for this website :) I am interested in sharing the code and however due to a recent change of computer I need to re-find that.

    Sorry for the delay.

    Best regards,

  5. Hi, I am very interestend in the code, this is one of the nicest tutorials on PDE on GPGPU i found so far.If you can please send me the source code i would appreciate it.
    Thank you.
    alienboal @ yahoo . com

  6. Hi. Could you please send me the code at my email:
    I will really appreciate your help.


  7. Hi Could You Send me the code at

    Thank you very much

  8. i need the code to do some experiment, could you send me to

  9. Hello!
    This post is very interesting, I am into a similar project, where I would like to use the CUDA platform to speed up my heat transfer and fluid flow analysis.
    I would like to view the code and understand the discretising process.


  10. Hello, I'm a student studying FDM with CUDA in Korea.
    Can you please send me this code? Your code will really help me.
    Please send me the code.
    Thanks a lot.