Dedalus Project

Dedalus accepts nearly arbitrary systems of differential equations and algebraic constraints entered in plain text. The linear terms are parsed into a sparse matrix system for efficient linear solves, and the nonlinear terms are parsed into arithmetic trees and evaluated pseudospectrally using matrix and fast transforms. The tau method is used to enforce nearly arbitrary boundary conditions, which are also entered in plain text.

Dedalus solves over domains that can be discretized with global spectral bases. Cartesian domains of any dimension can be built from the direct-product of the included one-dimensional bases. Curvilinear domains are supported using novel non-direct-product bases.

The separable dimensions of any problem are automatically parallelized across the available cores or a user-specified process mesh. We use MPI to coordinate parallelized computations, and have scaled Dedalus to thousands of processes.

Initial value problems are solved by spectrally discretizing the spatial domain, and evolving the coefficients as a system of coupled ordinary differential equations. Dedalus currently contains a range of ODE integrators including multistep and Runge-Kutta IMEX methods for implicit timestepping of the linear terms and explicit timestepping of the nonlinear terms. New methods are simple to implement.

The same symbolic format that is used to represent equations can also be used to specify analysis tasks, which are computed in concert with the nonlinear terms and saved in self-describing HDF5 files.