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Fix: some updates to naaice/README.md

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This directory contains a concise benchmark designed for validating FPGA This directory contains a concise benchmark designed for validating FPGA
offloading of the Thomas algorithm, primarily employed for solving linear offloading of the Thomas algorithm, primarily employed for solving linear
equation systems structured within a tridiagonal matrix. equation systems structured within a tridiagonal matrix.
@ -6,20 +5,19 @@ equation systems structured within a tridiagonal matrix.
# Benchmark Setup # Benchmark Setup
The benchmark involves a domain measuring $0.5 \text{cm} \times 1 \text{cm}$, The benchmark defines a domain measuring $1 \text{cm} \times 0.5 \text{cm}$ (easting $\times$ northing),
divided into a grid of dimensions $10 \times 5$. Each grid cell initially discretized in a $10 \times 5$ grid. Each grid cell initially
contains a specific concentration. The concentration in the first half along the contains a specific concentration. The concentration in the left domain half is set to $6.92023 \times 10^{-7}$, while in the right half to
x-dimension is set at $6.92023 \times 10^{-7}$, while in the second half, it’s $2.02396 \times 10^{-8}$, creating an horizontal concentration discontinuity at
$2.02396 \times 10^{-8}$, creating a concentration gradient along the y-axis at the center of the grid. These initial concentrations are read from headerless csv file [init_conc.csv](./init_conc.csv).
the center of the grid.
To achieve concentration equilibrium, we employ a simulation based on a A diffusion time step is simulated with the
heterogeneous 2D-ADI BTCS diffusion approach, detailed in the heterogeneous 2D-ADI approach detailed in the
[ADI<sub>scheme.pdf</sub>](../doc/ADI_scheme.pdf) file. In the x-direction, [ADI_scheme.pdf](../doc/ADI_scheme.pdf) file. The x component of the
diffusion coefficients range from $\alpha = 10^{-9}$ to $10^{-10}$, while in the diffusion coefficients, read from headerless csv file [alphax.csv](./alphax.csv) ranges from $\alpha = 10^{-9}$ to $10^{-10}$ (distributed randomly), while the
y-direction, a constant value of $5 \times 10^{-10}$ is applied. A closed y-component is held constant at $5 \times 10^{-10}$. Closed
boundary condition is implemented, meaning concentrations cannot enter or exit boundary conditions are enforced at all domain boundaries, meaning that concentration cannot enter or exit
the system. The diffusion process is simulated for a single iteration with a the system, or in other terms, that the sum of concentrations over the domain must stay constant. The benchmark simulates a single iteration with a
time step ($\Delta t$) of 360 seconds. time step ($\Delta t$) of 360 seconds.