Methodology

Dedalus Methods Paper

For details on the mathematical and computational methodologies underlying Dedalus v2, please consult the Dedalus methods paper:

K J Burns, G M Vasil, J S Oishi, D Lecoanet, B P Brown, “Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods,” Physical Review Research, vol. 2, no. 2, p. 838, Apr. 2020. [doi] [arxiv] [bibtex] [examples]

Curvilinear Bases

For details on the mathematics behind Dedalus’ bases for curvilinear domains, please consult the following papers:

G M Vasil, K J Burns, D Lecoanet, S Olver, B P Brown, J S Oishi, “Tensor calculus in polar coordinates using Jacobi polynomials,” Journal of Computational Physics, vol. 325, pp. 53-73, Nov 2016. [doi]

G M Vasil, D Lecoanet, K J Burns, J S Oishi, B P Brown, “Tensor calculus in spherical coordinates using Jacobi polynomials. Part-I: Mathematical analysis and derivations,” Journal of Computational Physics: X, vol. 3, p. 100013, Jun 2019. [doi]

D Lecoanet, G M Vasil, K J Burns, B P Brown, J S Oishi, ” Tensor calculus in spherical coordinates using Jacobi polynomials. Part-II: Implementation and examples,” J ournal of Computational Physics: X, vol. 3, p. 100012, Jun 2019. [doi]