....

You may be more familiar with the Laplace operator being written as $\nabla^2$, and written in the form

$$\nabla^2 u = \nabla^t \cdot \nabla u = \frac{\partial^2 u}{\partial x\hackscore 0^2} + \frac{\partial^2 u}{\partial x\hackscore 1^2}$$

and Equation (1.1) as

$$-\nabla^2 u = f$$

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....

Some readers may familiar with the notation $\frac{\partial u}{\partial n} = n\hackscore{i} u\hackscore{,i}$ for the normal derivative.

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... command

escript is not available under Windows yet. If you run under windows you can just use the python command and the OMP_NUM_THREADS environment variable to control the number of threads.

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... present.

There is a difference in esys.escript of being not present and set to zero. As not present coefficients are not processed, it is more efficient to leave a coefficient undefined instead of assigning zero to it.

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... way 

Please, note that this is not a complete code. The complete code can be found in ``helmholtz.py''.

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... command

The escript launcher is not supported under MS Windows yet.

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...FirstSteps

For this discussion, it is assumed that escript is included in your PATH environment. See installation guide for details.

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... nodes

For simplicity, we will use the term node to refer to either a node in a super computer or an individual machine in a cluster

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... set

That is, it has a non-empty value.

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... time

In case of OpenMP only one copy is running but esys.escript temporarily spawns threads.

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...$zero$

In fact it is assumed they are not present by assigning the value escript.Data(). The can by used by the solver library to reduce computational costs.

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... $SGI,~Reference~\cite{SCSL}$

The SCSL library will only be available on SGI systems

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... $Intel,~Reference~\cite{MKL}$

The MKL library will only be available when the Intel compilation environment is used.

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