TugJulia/naaice

This directory contains a concise benchmark designed for validating FPGA offloading of the Thomas algorithm, primarily employed for solving linear equation systems structured within a tridiagonal matrix.

Benchmark Setup

The benchmark involves a domain measuring 0.5 \text{cm} \times 1 \text{cm}, divided into a grid of dimensions 10 \times 5. Each grid cell initially contains a specific concentration. The concentration in the first half along the x-dimension is set at 6.92023 \times 10^{-7}, while in the second half, it’s 2.02396 \times 10^{-8}, creating a concentration gradient along the y-axis at the center of the grid.

To achieve concentration equilibrium, we employ a simulation based on a heterogeneous 2D-ADI BTCS diffusion approach, detailed in the ADI_scheme.pdf file. In the x-direction, diffusion coefficients range from \alpha = 10^{-9} to 10^{-10}, while in the y-direction, a constant value of 5 \times 10^{-10} is applied. A closed boundary condition is implemented, meaning concentrations cannot enter or exit the system. The diffusion process is simulated for a single iteration with a time step (\Delta t) of 360 seconds.

Setup

To generate new makefiles using the -DTUG_NAAICE_EXAMPLE=ON option in CMake, compile the executable, and run it to generate the benchmark output, follow these steps:

1. Navigate to your project's build directory.

2. Run the following CMake command with the -DTUG_NAAICE_EXAMPLE=ON option to generate the makefiles:

   cmake -DTUG_NAAICE_EXAMPLE=ON ..
   

3. After CMake configuration is complete, build the naaice executable by running make:

   make naaice
   

4. Once the compilation is successful, navigate to the build directory by cd <build_dir>/naaice

5. Finally, run the naaice executable to generate the benchmark output:

   ./naaice
   

Output Files

Thomas_<n>.csv

These files contain the values of the tridiagonal coefficient matrix A, where:

• Aa represents the leftmost value,
• Ab represents the middle value, and
• Ac represents the rightmost value of one row of the matrix.

Additionally, the corresponding values of the right-hand-side vector b are provided.

Since the 2D-ADI BTCS scheme processes each row first and then proceeds column-wise through the grid, each iteration is saved separately in consecutively numbered files.

BTCS_5_10_1.csv

The result of the simulation, separated by whitespaces!