Ghost nodes: Difference between revisions
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See the [[Ghost nodes (theory)]] page for what ghost nodes and how they are used. We will use them in this example to reliably solver a 3D mixed Dirichlet and Neumann problem on an irregular domain. | See the [[Ghost nodes (theory)]] page for what ghost nodes and how they are used. We will use them in this example to reliably solver a 3D mixed Dirichlet and Neumann problem on an irregular domain. | ||
We will solve the problem | |||
$\nabla^2 u = 1 \text{ in } \Omega, \quad \frac{\partial u}{\partial n} = 0 \text{ on } \partial \Omega_{+}, \quad u = 0 \text{ on } \partial \Omega_{-}$ | |||
where $\Omega = B(\boldsymbol{0}, 1) - B(\boldsymbol{1}, 1.5)$. | |||
Revision as of 12:22, 17 May 2019
See the Ghost nodes (theory) page for what ghost nodes and how they are used. We will use them in this example to reliably solver a 3D mixed Dirichlet and Neumann problem on an irregular domain.
We will solve the problem
$\nabla^2 u = 1 \text{ in } \Omega, \quad \frac{\partial u}{\partial n} = 0 \text{ on } \partial \Omega_{+}, \quad u = 0 \text{ on } \partial \Omega_{-}$
where $\Omega = B(\boldsymbol{0}, 1) - B(\boldsymbol{1}, 1.5)$.