Errata in published works

• 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 z₀ should read Im Z^-1(z₀). (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 Guimarães.)
• 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 10¹⁴
  • 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