diff --git a/naaice/README.md b/naaice/README.md index 54a2c95..b4f1f9d 100644 --- a/naaice/README.md +++ b/naaice/README.md @@ -1,4 +1,3 @@ - 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. @@ -6,20 +5,19 @@ 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. +The benchmark defines a domain measuring $1 \text{cm} \times 0.5 \text{cm}$ (easting $\times$ northing), +discretized in a $10 \times 5$ grid. Each grid cell initially +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 +$2.02396 \times 10^{-8}$, creating an horizontal concentration discontinuity at +the center of the grid. These initial concentrations are read from headerless csv file [init_conc.csv](./init_conc.csv). -To achieve concentration equilibrium, we employ a simulation based on a -heterogeneous 2D-ADI BTCS diffusion approach, detailed in the -[ADIscheme.pdf](../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 +A diffusion time step is simulated with the +heterogeneous 2D-ADI approach detailed in the +[ADI_scheme.pdf](../doc/ADI_scheme.pdf) file. The x component of 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-component is held constant at $5 \times 10^{-10}$. Closed +boundary conditions are enforced at all domain boundaries, meaning that concentration cannot enter or exit +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.