C++ for Scientists - Technische Universität Dresden

Numerical exercises
Chapter 14
In this chapter, we list a number of exercises where the different aspects discussed in the course
will be used. The goal is to implement a small application program in C++, run it and interpret
the results.
You can use any software that may help you with your task. A list of packages is provided
at the end of this chapter. We have only installed Boost, Boost.Sandbox, GLAS, BLAS, and,
LAPACK. Other smaller packages could be downloaded if necessary.
In each exercise, a generic function or class will be developed, and its documentation. These
functions and classes should be part of the namespace athens. The functions arguments will
have to be described. Each template argument will have to satisfy concepts. You may have
to define new concepts. If you are using STL or GLAS concepts, you can just refer to them,
without definition.
Write a small paper on the decisions you made for the development of the software. Use the
software for some examples and report the results. You may write the report on paper or send
it in electronic form (PDF by preference).
14.1 Computing an eigenfunction of the Poisson equation
This is an example of a more complicated problem. It illustrates what is expected from the
exercises. The actual exercises are less demanding.
In this section, we derive software for the solution of the Poisson equation. We start with the
1D problem and then move to the 2D problem.
14.1.1 The 1D Poisson equation
The 1D Poisson equation is
− d2u = f (14.1)
dx2 where u(x) is the solution and f the excitation and x ∈ [0, 1]. We impose the boundary
conditions
u(0) = u(1) = 0 .
263