Overview of this book

Learning SciPy for Numerical and Scientific Computing Second Edition
Credits
www.PacktPub.com
Preface
Free Chapter
Introduction to SciPy
Working with the NumPy Array As a First Step to SciPy
SciPy for Linear Algebra
SciPy for Numerical Analysis
SciPy for Signal Processing
SciPy for Data Mining
SciPy for Computational Geometry
Interaction with Other Languages
Index

A finite element solver for Laplace's equation

We use finite elements when the size of the data is so large that its results prohibit dealing with finite differences. To illustrate this case, we would like to explore the numerical solution of the Laplace equation, subject to certain boundary conditions.

We will start by defining the computational domain and produce a mesh dividing this domain using triangles as local finite elements. This will be our starting point to solve this problem using finite elements, as we will be placing on the computational domain a piecewise continuous function, whose pieces are linear and supported on each of the triangles.

We start by calling the necessary modules to build the mesh (other modules will be called as they are required):

```>>> import numpy
>>> from numpy import linspace
>>> import scipy
>>> import matplotlib.pyplot as plt
>>> from scipy.spatial import Delaunay
```

First we define the region:

`>>> xmin...`