#+title: NAAICE Benchmark

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 [[file:../doc/ADI_scheme.pdf][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:

    #+BEGIN_SRC sh
    cmake -DTUG_NAAICE_EXAMPLE=ON ..
    #+END_SRC

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

    #+BEGIN_SRC sh
    make naaice
    #+END_SRC

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:

    #+BEGIN_SRC sh
    ./naaice
    #+END_SRC

** 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*!