3-d problems

The techniques discussed in Sects. 5.7 and 5.8 for solving Poisson's equation in two dimensions with a restricted class of boundary conditions can easily be generalized to three dimensions. In the 3-d case, it is necessary to Fourier transform in two directions (the $y$ and $z$ directions, say) in order to reduce the problem to a system of uncoupled tridiagonal matrix equations. These equations can be inverted in the usual manner, and the solution can then be reconstructed via a double inverse Fourier transform.