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<sub>scheme.pdf</sub>](../doc/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.


# Usage

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**!