Fast Solution of Fully Implicit Runge-Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting

  title={Fast Solution of Fully Implicit Runge-Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting},
  author={Ben S. Southworth and Oliver A. Krzysik and Will Pazner and Hans De Sterck},
  journal={SIAM J. Sci. Comput.},
Fully implicit Runge-Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but are rarely used in practice with numerical PDEs due to the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic preconditioning framework for solving the systems of equations that arise from IRK methods applied to linear numerical PDEs (without algebraic constraints). This framework also naturally applies to… 

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