Year: 2018
Type: article
Abstract: The efficient solution of discretizations of coupled systems of partial differential equations (PDEs) is at the core of much of numerical simulation. Significant effort has been expended on scalable algorithms to precondition Krylov iterations for the linear systems that arise. With few exceptions, the reported numerical implementation of such solution strategies is specific to a particular model setup, and intimately ties the solver strategy to the discretization and PDE, especially when the preconditioner requires auxiliary operators. In this paper, we present recent improvements in the Firedrake finite element library that allow for straightforward development of the building blocks of extensible, composable preconditioners that decouple the solver from the model formulation. Our implementation extends the algebraic composability of linear solvers offered by the PETSc library by augmenting operators, and hence preconditioners, with the ability to provide any necessary auxiliary operators. Rather than specifying up front the full solver configuration tied to the model, solvers can be developed independently of model formulation and configured at runtime. We illustrate with examples from incompressible fluids and temperature-driven convection.
DOI: 10.1137/17m1133208
Authors: Robert C. Kirby, Lawrence Mitchell
Institutions: Baylor University, Imperial College London
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W2622013296