Jordan-curve coefficient-growth conjecture for the Method of Fundamental Solutions

Let $Omega$ be the domain of the Helmholtz boundary-value problem, and let $Gamma$ be any Jordan curve enclosing $\overline{\Omega}$ with positive distance from $\partial\Omega$. Choose MFS charge points on $Gamma$ asymptotically densely, and let $\boldsymbol{\alpha}$ be the coefficient vector minimizing the MFS error $t$. Jordan-curve coefficient-growth conjecture. The norm $|\boldsymbol{\alpha}|$ grows asymptotically exponentially as $N\to\infty$ if and only if $Gamma$ encloses a singularity of the analytic continuation of $u$. This is a proposed generalization of the conformal-radius observation to arbitrary charge-point curves; the paper reports numerical evidence and relates it to known scattering results.