Extending <tt>Irksome</tt> : Improvements in Automated Runge–Kutta Time Stepping for Finite Element Methods
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Bibliographic record
Abstract
Irksome is a library based on the Unified Form Language (UFL) that enables automated generation of Runge–Kutta methods for time-stepping finite element spatial discretizations of Partial Differential Equations (PDEs). Allowing users to express semidiscrete forms of PDEs, it generates UFL representations for the stage-coupled variational problems to be solved at each timestep. The Firedrake package then generates efficient code for evaluating these variational problems and allows users a wide range of options to deploy efficient algebraic solvers in PETSc. In this article, we describe several recent advances in Irksome . These include alternate formulations of the Runge–Kutta time-stepping methods and optimized support for diagonally implicit (DIRK) methods. Additionally, we present new and improved tools for building preconditioners for the resulting linear and linearized systems, demonstrating that these can lead to efficient approaches for solving fully implicit Runge–Kutta discretizations. The new features are demonstrated through a sequence of computational examples demonstrating the high-level interface and obtained solver performance.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
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| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
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| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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