Dedalus: A flexible framework for numerical simulations with spectral methods
Abstract
Numerical solutions of partial differential equations enable a broad range of scientific research. The Dedalus project is a flexible, opensource, parallelized computational framework for solving general partial differential equations using spectral methods. Dedalus translates plaintext strings describing partial differential equations into efficient solvers. This paper details the numerical method that enables this translation, describes the design and implementation of the codebase, and illustrates its capabilities with a variety of example problems. The numerical method is a firstorder generalized tau formulation that discretizes equations into banded matrices. This method is implemented with an objectoriented design. Classes for spectral bases and domains manage the discretization and automatic parallel distribution of variables. Discretized fields and mathematical operators are symbolically manipulated with a basic computer algebra system. Initial value, boundary value, and eigenvalue problems are efficiently solved using highperformance linear algebra, transform, and parallel communication libraries. Custom analysis outputs can also be specified in plain text and stored in selfdescribing portable formats. The performance of the code is evaluated with a parallel scaling benchmark and a comparison to a finitevolume code. The features and flexibility of the codebase are illustrated by solving several examples: the nonlinear Schrödinger equation on a graph, a supersonic magnetohydrodynamic vortex, quasigeostrophic flow, Stokes flow in a cylindrical annulus, normal modes of a radiative atmosphere, and diamagnetic levitation.
 Publication:

Physical Review Research
 Pub Date:
 April 2020
 DOI:
 10.1103/PhysRevResearch.2.023068
 arXiv:
 arXiv:1905.10388
 Bibcode:
 2020PhRvR...2b3068B
 Keywords:

 Astrophysics  Instrumentation and Methods for Astrophysics;
 Physics  Computational Physics;
 Physics  Fluid Dynamics
 EPrint:
 40 pages, 18 figures. Accepted to Physical Review Research