  An Ewald decomposition of the two-dimensional Yukawa potential and its
derivative is presented for both the periodic and the free-space case. These
modified Bessel functions of the second kind of zeroth and first degrees are
used e.g. when solving the modified Helmholtz equation using a boundary
integral method. The spectral Ewald method is used to compute arising sums at
O(N log N) cost for N source and target points. To facilitate parameter
selection, truncation-error estimates are developed for both the real-space sum
and the Fourier-space sum, and are shown to estimate the errors well.
