/
poisson.tsx
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/
poisson.tsx
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/** @module Models.Description.Poisson */
import ReactDOMServer from 'react-dom/server'
import MathJax from '@/components/assets/mathjax'
// Description
const description = (
<>
<h3>Poisson's equation</h3>
<div>
Let <MathJax.BackInline text={'\\Omega'} /> be a domain of{' '}
<MathJax.BackInline text={'\\mathbb{R}^{d}'} />, with{' '}
<MathJax.BackInline text={'d\\in\\{2,3\\}'} />.
</div>
<div>
The domain <MathJax.BackInline text={'\\Omega'} /> is bounded by{' '}
<MathJax.BackInline text={'\\Gamma = \\Gamma_D \\cup \\Gamma_N'} />.
</div>
<div>
The Poisson's equation reads as follow:
<MathJax.BackFormula
text={`
\\begin{align}
\\Delta u &= f &\\text{on }\\Omega\\\\
u &= u_D &\\text{on }\\Gamma_D\\\\
\\nabla u &= g_N &\\text{on }\\Gamma_N
\\end{align}
`}
/>
</div>
<figure>
<img src="/images/Poisson.png" alt="Poisson" />
<figcaption>Poisson's equation example on a cube.</figcaption>
</figure>
<div>
See{' '}
<a
target="_blank"
href="https://en.wikipedia.org/wiki/Poisson%27s_equation"
>
Wikipedia
</a>
{/**/}.
</div>
</>
)
export default ReactDOMServer.renderToString(description)