In my research I mostly work with the Julia programming language and most of the software I produce tends to be different kinds of Julia packages. You can find most of my packages on GitHub, some of the more important ones are also listed below.

Arblib.jl

Arblib is a Julia package in the public repository which aims to be a thin and efficient wrapper around Arb - a C library for arbitrary-precision ball arithmetic. I’m one of the main developers, together with Marek Kaluba and Sascha Timme.

MethodOfParticularSolutions.jl

L-shaped domain

A Julia package for computing eigenvalues and eigenfunctions of the Laplacian on planar or spherical domains using the method of particular solutions. This package has mainly been written for use in specific projects and is not very suitable for general usage.

  1. Dahne, J., Gómez-Serrano, J., & Hou, K. (2021). A counterexample to Payne’s nodal line conjecture with few holes. Commun. Nonlinear Sci., 103(), 105957.
  2. Dahne, J., & Salvy, B., Computation of tight enclosures for laplacian eigenvalues, SIAM Journal on Scientific Computing, 42(5), 3210–3232 (2020).

PaynePolygon.jl

Counterexample to Payne's conjecture

The computer assisted proof accompanying the paper

Dahne, J., Gómez-Serrano, J., & Hou, K. (2021). A counterexample to Payne’s nodal line conjecture with few holes. Commun. Nonlinear Sci., 103(), 105957.

BurgersHilbertWave.jl

The computer assisted proof accompanying the paper

Dahne, J., Gómez-Serrano, J., Highest Cusped Waves for the Burgers-Hilbert equation (2022)