Errata in published works
Please email me with any mistakes you find in my published works.
Here are the ones I know about (fortunately they are all minor details):
- Accurate close interactions of Stokes spheres using
lubrication-adapted image systems,
A. Broms, A. H. Barnett, and A.-K. Tornberg, J. Comput. Phys.
523 (2025) 113636.
Fig. 2(a) the labels xi and yj
should be swapped.
- Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects,
D. B. Stein and A. H. Barnett.
Adv. Comput. Math. 48, article 60 (2022).
Sec. 2.4, paragraph after (28): in d=2 the constant
term ω may be extracted from the far field solution via
subtraction of
[log r - r rT/r2]
Σ,
i.e., a scaled stokeslet, rather than merely Σ log r
as claimed.
- 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