heat

Heat equation solver parallelized with OpenACC

Create a parallel version of a heat equation solver using OpenACC.

Starting from a serial heat equation solver (see below for details), port the code to GPUs using OpenACC in two steps.

1. Use OpenACC to parallelize the time evolution loop in the heat equation solver.
2. Improve the OpenACC version by adding data movement directives to minimise data transfers between the host CPU and the GPU device.

Heat equation solver

The heat equation is a partial differential equation that describes the variation of temperature in a given region over time

where u(x, y, z, t) represents temperature variation over space at a given time, and α is a thermal diffusivity constant.

We limit ourselves to two dimensions (plane) and discretize the equation onto a grid. Then the Laplacian can be expressed as finite differences as

Where ∆x and ∆y are the grid spacing of the temperature grid u(i,j). We can study the development of the temperature grid with explicit time evolution over time steps ∆t:

There are a solver for the 2D equation implemented with Fortran (including some C for printing out the images). You can compile the program by adjusting the Makefile as needed and typing make. The solver carries out the time development of the 2D heat equation over the number of time steps provided by the user. The default geometry is a flat rectangle (with grid size provided by the user), but other shapes may be used via input files. Examples on how to run the binary:

• ./heat No arguments - the program will run with the default arguments: 200 x 200 grid and 500 time steps
• ./heat bottle.dat One argument - start from a temperature grid provided in the file bottle.dat for the default number of time steps.
• ./heat bottle.dat 1000 Two arguments - will run the program starting from a temperature grid provided in the file bottle.dat for 1000 time steps
• ./heat 1024 2048 1000 Three arguments - will run the program in a 1024x2048 grid for 1000 time steps.

The program will produce a .png image of the temperature field after every 100 iterations. You can change that from the parameter image_interval. You can visualise the images using the command animate: animate heat_*.png, or by using eog heat_000.png and using the arrow-keys to loop backward or forward through the files.