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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
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
[ADI<sub>scheme.pdf</sub>](../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.