# Errata in published works

Please email me with any mistakes you find in my published works.
Here are the ones I know about.
**Evaluation of layer potentials close to the boundary
for Laplace and Helmholtz problems on analytic planar domains**,
A. H. Barnett, *SIAM J. Sci. Comput.*
**36**(2), A427-A451 (2014).
On p. A439, in the statement of Theorem 3.2, Im *z*_{0} should read
Im *Z*^{-1}(*z*_{0}).
(Thanks to Hasan Majidian.)
**Fast computation of high frequency Dirichlet eigenmodes via the spectral flow of the interior Neumann-to-Dirichlet map**,
A. H. Barnett and A. Hassell,
*Comm. Pure Appl. Math.* **67**(3), 351-407 (2014).
The polar coordinates definition of the domain in caption of Figure 1
is wrong: the innermost sin should be cos.
Thus the shape is
r(θ) = 1 + 0.3 cos [3 (θ + 0.2 cos θ)].
It is correct in the MPSpack code `smoothnonsym`

linked in the
paper.
(Thanks to Osvaldo GuimarĂ£es.)
**Stability and convergence of the Method of Fundamental Solutions for Helmholtz problems on analytic domains**, A. H. Barnett and T. Betcke,
*J. Comput. Phys.* **227**(14), 7003-7026 (2008).
Equation (22) would only hold in the case of boundary data arising from a
simple pole Re(*z*-ρ)^{-1}. For a general singularity
there would be algebraic terms. A simple fix would be to assume (22) holds,
but amend the text to the stronger condition that the closest singularity be ρ+ε for some positive ε.
(Thanks to Urve Kangro.)
- Ph.D Thesis,
**Dissipation in Deforming Chaotic Billiards** (Harvard University, 2000).
- missing factor of 1/2k^2 in Eqn H7
- equation reference numbers a b c jumbled in I.9abc
- typo App B.2, p.161, C_F(omega)
- typo App. J, bottom of 1st page, should be 10
^{14}
- Sec. 6.1.3 (p.88): in "Use of a scaling basis": eps_mu(k;
**r**) not (k;**k**)
- ...and, unconvincing derivation of Fokker-Planck in App. A