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:

Navigate to your project's build directory.
Run the following CMake command with the -DTUG_NAAICE_EXAMPLE=ON option to generate the makefiles:
```
cmake -DTUG_NAAICE_EXAMPLE=ON ..
```
After CMake configuration is complete, build the naaice executable by running make:
```
make naaice
```
Once the compilation is successful, navigate to the build directory by cd <build_dir>/naaice
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!