PiTSBiCG: Parallel in time Stable Bi-Conjugate gradient algorithm

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Abstract

This paper presents a new algorithm for the parallel in time (PiT) numerical simulation of time dependent partial/ordinary differential equations. We propose a reliable alternative to the well know parareal in time algorithm, by formulating the parallel in time problem algebraically and solve it using an adapted Bi-Conjugate gradient stabilized method. The proposed Parallel in time Stable Bi-Conjugate algorithm (PiTSBiCG for short) has a great potential to stabilizing the parallel resolution for a variety of problems. In this work, we describe the mathematical approach to the new algorithm and provide numerical evidence that shows its superiority to the standard parareal method.

Original languageBritish English
Pages (from-to)225-233
Number of pages9
JournalApplied Numerical Mathematics
Volume181
DOIs
StatePublished - Nov 2022

Keywords

  • Acceleration
  • BiCGStab
  • Krylov methods
  • Numerical simulation of PDEs
  • Parallel computing
  • Parallel in time algorithm
  • Parareal

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