....

Some readers 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 (2.1) as

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

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

....

Some readers may familiar with the notation

$$\frac{\partial u}{\partial n} = n\hackscore{i} u\hackscore{,i}$$

for the normal derivative.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... 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.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...$zero$

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.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... $Reference \cite{SCSL}$

The SCSL library will only be available on SGI systems

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... $Reference \cite{MKL}$

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

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.