ADDiffusion.md

ADDiffusion

Description

The steady-state diffusion equation on a domain $\Omega$ is defined as \begin{equation} -\nabla \cdot \nabla u = 0 \in \Omega. \end{equation}

The weak form of this equation, in inner-product notation, is given by:

\begin{equation} R_i(u_h) = (\nabla \psi_i, \nabla u_h) = 0 \quad \forall \psi_i, \end{equation} where $\psi_i$ are the test functions and $u_h \in \mathcal{S}^h$ is the finite element solution of the weak formulation.

The Jacobian in ADDiffusion is computed using forward automatic differentiation.

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