A New Block Preconditioner for Implicit Runge--Kutta Methods for Parabolic PDE Problems

DOI10.1137/20M1349680MaRDI QIDQ5161755

Md Masud Rana, Ashley Meek, Katharine Long, William Milestone, Victoria E. Howle

Publication date: 1 November 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.11377

zbMATH Keywords

preconditioningparabolic PDEimplicit Runge-Kutta

Mathematics Subject Classification ID

Preconditioners for iterative methods (65F08)

Related Items (6)

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting ⋮ Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs ⋮ Additive Polynomial Time Integrators, Part I: Framework and Fully Implicit-Explicit Collocation Methods ⋮ Theoretical and practical aspects of space-time DG-SEM implementations ⋮ Monolithic multigrid for implicit Runge-Kutta discretizations of incompressible fluid flow ⋮ A-Stable High-Order Block Implicit Methods for Parabolic Equations

Uses Software

• RODAS
• IFISS

Cites Work

• On some techniques for approximating boundary conditions in the finite element method
• Nitsche’s method for general boundary conditions
• Solving Ordinary Differential Equations I
• Unified Embedded Parallel Finite Element Computations via Software-Based Fréchet Differentiation
• Order‐Optimal Preconditioners for Implicit Runge–Kutta Schemes Applied to Parabolic PDEs
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