Abstract
Modern high performance computers are massively parallel; for many PDE
applications spatial parallelism saturates long before the computer's
capability is reached. Parallel-in-time methods enable further speedup beyond
spatial saturation by solving multiple timesteps simultaneously to expose
additional parallelism. ParaDiag is a particular approach to parallel-in-time
based on preconditioning the simultaneous timestep system with a perturbation
that allows block diagonalisation via a Fourier transform in time. In this
article, we introduce asQ, a new library for implementing ParaDiag
parallel-in-time methods, with a focus on applications in the geosciences,
especially weather and climate. asQ is built on Firedrake, a library for the
automated solution of finite element models, and the PETSc library of scalable
linear and nonlinear solvers. This enables asQ to build ParaDiag solvers for
general finite element models and provide a range of solution strategies,
making testing a wide array of problems straightforward. We use a quasi-Newton
formulation that encompasses a range of ParaDiag methods, and expose building
blocks for constructing more complex methods. The performance and flexibility
of asQ is demonstrated on a hierarchy of linear and nonlinear atmospheric flow
models. We show that ParaDiag can offer promising speedups and that asQ is a
productive testbed for further developing these methods.