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The peak heat flux conjecture for the first Dirichlet eigenmode of convex planar domains
Zijian Wang, Jeremy G. Hoskins, Manas Rachh +1
In this paper, we study the scale-invariant quantity \[\mathcal{G}(Ω)=\frac{\|\partial_n u_1\|_{L^\infty(\partialΩ)}}{λ_1},\]where is the first -normalized Dirichlet Lap…
A fully adaptive, high-order, fast Poisson solver for complex two-dimensional geometries
Daniel Fortunato, David B. Stein, Alex H. Barnett
We present a new framework for the fast solution of inhomogeneous elliptic boundary value problems in domains with smooth boundaries. High-order solvers based on adaptive box codes…
Superfast direct inversion of the nonuniform discrete Fourier transform via hierarchically semi-separable least squares
Heather Wilber, Ethan N. Epperly, Alex H. Barnett
A direct solver is introduced for solving overdetermined linear systems involving nonuniform discrete Fourier transform matrices. Such matrices can be transformed into a Cauchy-lik…
Trapped acoustic waves and raindrops: high-order accurate integral equation method for localized excitation of a periodic staircase
Fruzsina J. Agocs, Alex H. Barnett
We present a high-order boundary integral equation (BIE) method for the frequency-domain acoustic scattering of a point source by a singly-periodic, infinite, corrugated boundary.…