asQ: parallel-in-time finite element simulations using ParaDiag for geoscientific models and beyond

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.

v2: 32 pages, 15 figures. Submitted to journal. Updated results with Zenodo software archives

References in corpus (16)

• Wave propagation characteristics of Parareal
• Solver composition across the PDE/linear algebra barrier
• Automated generation and symbolic manipulation of tensor product finite elements
• PCPATCH: software for the topological construction of multigrid relaxation methods
• Optimizing multigrid reduction-in-time (MGRIT) and Parareal coarse-grid operators for linear advection
• A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake
• Parallel-in-Time Multi-Level Integration of the Shallow-Water Equations on the Rotating Sphere
• Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond
• Achieving Efficient Strong Scaling with PETSc using Hybrid MPI/OpenMP Optimisation
• A Parallel Time-Integrator for Solving the Linearized Shallow Water Equations on the Rotating Sphere
• Twelve Ways To Fool The Masses When Giving Parallel-In-Time Results
• Multigrid reduction-in-time convergence for advection problems: A Fourier analysis perspective
• Parallel-in-time solution of hyperbolic PDE systems via characteristic-variable block preconditioning
• A parallel-in-time collocation method using diagonalization: theory and implementation for linear problems
• Stability implies robust convergence of a class of preconditioned parallel-in-time iterative algorithms
• Extending Irksome: improvements in automated Runge--Kutta time stepping for finite element methods