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73 lines
2.5 KiB
Markdown
73 lines
2.5 KiB
Markdown
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This directory contains a concise benchmark designed for validating FPGA
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offloading of the Thomas algorithm, primarily employed for solving linear
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equation systems structured within a tridiagonal matrix.
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# Benchmark Setup
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The benchmark involves a domain measuring $0.5 \text{cm} \times 1 \text{cm}$,
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divided into a grid of dimensions $10 \times 5$. Each grid cell initially
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contains a specific concentration. The concentration in the first half along the
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x-dimension is set at $6.92023 \times 10^{-7}$, while in the second half, it’s
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$2.02396 \times 10^{-8}$, creating a concentration gradient along the y-axis at
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the center of the grid.
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To achieve concentration equilibrium, we employ a simulation based on a
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heterogeneous 2D-ADI BTCS diffusion approach, detailed in the
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[ADI<sub>scheme.pdf</sub>](../doc/ADI_scheme.pdf) file. In the x-direction,
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diffusion coefficients range from $\alpha = 10^{-9}$ to $10^{-10}$, while in the
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y-direction, a constant value of $5 \times 10^{-10}$ is applied. A closed
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boundary condition is implemented, meaning concentrations cannot enter or exit
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the system. The diffusion process is simulated for a single iteration with a
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time step ($\Delta t$) of 360 seconds.
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# Usage
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To generate new makefiles using the `-DTUG_NAAICE_EXAMPLE=ON` option in CMake,
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compile the executable, and run it to generate the benchmark output, follow
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these steps:
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1. Navigate to your project's build directory.
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2. Run the following CMake command with the `-DTUG_NAAICE_EXAMPLE=ON` option to
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generate the makefiles:
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cmake -DTUG_NAAICE_EXAMPLE=ON ..
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3. After CMake configuration is complete, build the `naaice` executable by running `make`:
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make naaice
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4. Once the compilation is successful, navigate to the build directory by `cd
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<build_dir>/naaice`
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5. Finally, run the `naaice` executable to generate the benchmark output:
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./naaice
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## Output Files
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### `Thomas_<n>.csv`
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These files contain the values of the tridiagonal coefficient matrix $A$, where:
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- $Aa$ represents the leftmost value,
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- $Ab$ represents the middle value, and
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- $Ac$ represents the rightmost value of one row of the matrix.
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Additionally, the corresponding values of the right-hand-side vector $b$ are
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provided.
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Since the 2D-ADI BTCS scheme processes each row first and then proceeds
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column-wise through the grid, each iteration is saved separately in
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consecutively numbered files.
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### `BTCS_5_10_1.csv`
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The result of the simulation, **separated by whitespaces**!
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