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Extending Irksome: improvements in automated Runge–Kutta time stepping for finite element methods

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Recent advancements improve runge-kutta time-stepping methods for finite element numerical solutions, streamlining computational efficiency.
New formulations and optimized diagonally implicit methods enhance performance in solving variations of PDEs efficiently.
This work employs the unified form language to create efficient representations, integrating with the Firedrake package for streamlined evaluation.
Preconditioner development is showcased, indicating potential for effective solutions to linear systems arising from implicit discretizations.

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Automated techniques enhance solver performance in finite element methods for partial differential equations, suggesting efficiency gains.

Kirby et al. (2025) studied this question.

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Automated techniques enhance solver performance in finite element methods for partial differential equations, suggesting efficiency gains.