 # Diff of /trunk/doc/cookbook/onedheatdiff001.tex

revision 2866 by gross, Thu Jan 21 04:45:39 2010 UTC revision 2867 by gross, Fri Jan 22 06:28:02 2010 UTC
# Line 164  which is used everywhere on the boundary Line 164  which is used everywhere on the boundary
164  Notice that the coefficient $A$ is the same as in the \esc PDE~\ref{eqn:commonform nabla}.  Notice that the coefficient $A$ is the same as in the \esc PDE~\ref{eqn:commonform nabla}.
165  With the settings for the coefficients we have already identified in \refEq{ESCRIPT SET} this  With the settings for the coefficients we have already identified in \refEq{ESCRIPT SET} this
166  condition translates into  condition translates into
167  \begin{equation}\label{NEUMAN 2}  \begin{equation}\label{NEUMAN 2b}
168  \kappa \frac{\partial T}{\partial x} = 0  \kappa \frac{\partial T}{\partial x} = 0
169  \end{equation}  \end{equation}
170  for the right hand side of the rod. This is identical to the Neuman boundary condition we want to set. \esc will take care of this condition for us. We will discuss the Dirichlet boundary condition later.  for the right hand side of the rod. This is identical to the Neuman boundary condition we want to set. \esc will take care of this condition for us. We will discuss the Dirichlet boundary condition later.
171

172  \subsection{A \textit{1D} Clarification}  \subsection{A \textit{1D} Clarification}
173  It is necessary for clarification that we revisit the general PDE from \refeq{eqn:commonform nabla} under the light of a two dimensional domain. \esc is inherently designed to solve problems that are greater than one dimension and so \refEq{eqn:commonform nabla} needs to be read as a higher dimensional problem. In the case of two spatial dimensions the \textit{Nabla operator} has in fact two components $\nabla = (\frac{\partial}{\partial x}, \frac{\partial}{\partial y})$. In full, \refEq{eqn:commonform nabla} assuming a constant coefficient $A$, takes the form;  It is necessary for clarification that we revisit the general PDE from \refeq{eqn:commonform nabla} under the light of a two dimensional domain. \esc is inherently designed to solve problems that are greater than one dimension and so \refEq{eqn:commonform nabla} needs to be read as a higher dimensional problem. In the case of two spatial dimensions the \textit{Nabla operator} has in fact two components $\nabla = (\frac{\partial}{\partial x}, \frac{\partial}{\partial y})$. In full, \refEq{eqn:commonform nabla} assuming a constant coefficient $A$, takes the form;
174  \begin{equation}\label{eqn:commonform2D}  \begin{equation}\label{eqn:commonform2D}
# Line 190  shown in \refEq{eqn:commonform} we need Line 187  shown in \refEq{eqn:commonform} we need
187  A\hackscore{00}=A; A\hackscore{01}=A\hackscore{10}=A\hackscore{11}=0  A\hackscore{00}=A; A\hackscore{01}=A\hackscore{10}=A\hackscore{11}=0
188  \end{equation}  \end{equation}
189
190    \subsection{Outline of the PDE Solution Script}
191
192
193
194  \subsection{Developing a PDE Solution Script}  \subsection{Developing a PDE Solution Script}
195  \label{sec:key}  \label{sec:key}
196  To solve the heat diffusion equation (equation \refEq{eqn:hd}) we will write a simple \pyt script which uses the \modescript, \modfinley and \modmpl modules. At this point we assume that you have some basic understanding of the \pyt programming language. If not there are some pointers and links available in Section \ref{sec:escpybas} .  To solve the heat diffusion equation (equation \refEq{eqn:hd}) we will write a simple \pyt script which uses the \modescript, \modfinley and \modmpl modules. At this point we assume that you have some basic understanding of the \pyt programming language. If not there are some pointers and links available in Section \ref{sec:escpybas} .

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