From 72107c944d452eb284971234dbdf524c1f789c85 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Max=20L=C3=BCbke?= <mluebke@uni-potsdam.de>
Date: Wed, 6 Sep 2023 14:21:22 +0200
Subject: [PATCH] Add readme

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+#+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*!