Commit 4130d460 authored by Philipp Nuske's avatar Philipp Nuske
Browse files

change in Newton in a Nutshell:

it makes a difference whether a matrix is multiplied from right or from
left. Hint from Nicolas.


git-svn-id: svn://svn.iws.uni-stuttgart.de/DUMUX/dumux/trunk@8950 2fb0f335-1f38-0410-981e-8018bf24f1b0
parent 98d25971
......@@ -24,8 +24,8 @@ One step of the \textsc{Newton} method can be formalized as follows:
\begin{align}
\label{NewtonGen}
\textbf{u}^{r+1} &= \textbf{u}^r - \left(\textbf{f}^\prime (\textbf{u}^r) \right)^{-1} \textbf{f}(\textbf{u}^r) \\
\Leftrightarrow ( \textbf{u}^{r+1}-\textbf{u}^r) {\textbf{f}^{\prime}(\textbf{u}^r)} &= -\textbf{f}(\textbf{u}^r) \\
\Leftrightarrow ( \textbf{u}^r - \textbf{u}^{r+1}) \underbrace{\textbf{f}^{\prime}(\textbf{u}^r)}_{\textnormal{Jacobian}} &= \textbf{f}(\textbf{u}^r) \label{NewtonAsUsed}
\Leftrightarrow {\textbf{f}^{\prime}(\textbf{u}^r)} ( \textbf{u}^{r+1}-\textbf{u}^r) &= -\textbf{f}(\textbf{u}^r) \\
\Leftrightarrow \underbrace{\textbf{f}^{\prime}(\textbf{u}^r)}_{\textnormal{Jacobian}} ( \textbf{u}^r - \textbf{u}^{r+1}) &= \textbf{f}(\textbf{u}^r) \label{NewtonAsUsed}
\end{align}
\end{subequations}
......
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment