Book Image

Learning SciPy for Numerical and Scientific Computing

By : Francisco J. Blanco-Silva
Book Image

Learning SciPy for Numerical and Scientific Computing

By: Francisco J. Blanco-Silva

Overview of this book

<p>It's essential to incorporate workflow data and code from various sources in order to create fast and effective algorithms to solve complex problems in science and engineering. Data is coming at us faster, dirtier, and at an ever increasing rate. There is no need to employ difficult-to-maintain code, or expensive mathematical engines to solve your numerical computations anymore. SciPy guarantees fast, accurate, and easy-to-code solutions to your numerical and scientific computing applications.<br /><br />"Learning SciPy for Numerical and Scientific Computing" unveils secrets to some of the most critical mathematical and scientific computing problems and will play an instrumental role in supporting your research. The book will teach you how to quickly and efficiently use different modules and routines from the SciPy library to cover the vast scope of numerical mathematics with its simplistic practical approach that's easy to follow.<br /><br />The book starts with a brief description of the SciPy libraries, showing practical demonstrations for acquiring and installing them on your system. This is followed by the second chapter which is a fun and fast-paced primer to array creation, manipulation, and problem-solving based on these techniques.<br /><br />The rest of the chapters describe the use of all different modules and routines from the SciPy libraries, through the scope of different branches of numerical mathematics. Each big field is represented: numerical analysis, linear algebra, statistics, signal processing, and computational geometry. And for each of these fields all possibilities are illustrated with clear syntax, and plenty of examples. The book then presents combinations of all these techniques to the solution of research problems in real-life scenarios for different sciences or engineering — from image compression, biological classification of species, control theory, design of wings, to structural analysis of oxides.</p>
Table of Contents (15 chapters)

A finite element solver for Poisson's equation


We use finite elements when the size of the data is so large that it results prohibitive to deal with finite differences. To illustrate this case, we would like to explore the potential flow over a wing, as a solution to the Laplace equation subjects to certain boundary conditions.

We wish to create a simple profile of a wing, and produce a mesh surrounding it. This will be our starting point to solve this problem using finite elements, as we will be placing on the domain a piecewise continuous function, whose pieces are linear and supported on each of the triangles.

import numpy
from numpy import pi, cos, sin, hstack, vstack, linspace, where
from numpy import ones, multiply, cross, array, mat, zeros, mgrid
import scipy
import matplotlib.pyplot as plt
from scipy.special import exp10
from scipy.linalg import norm
from scipy.sparse import dok_matrix
from scipy.sparse.linalg import spsolve
from scipy.interpolate import LinearNDInterpolator
from...