English

PiTSBiCG: Parallel in Time Stable Bi-Conjugate Gradient Algorithm

Numerical Analysis 2022-03-22 v1 Numerical Analysis Optimization and Control

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) has a great potential in stabilizing the parallel resolution for a variety of problems. In this work, we describe the mathematical approach to the new algorithm and provide numerical evidences that show its superiority to the standard parareal method.

Keywords

Cite

@article{arxiv.2203.10148,
  title  = {PiTSBiCG: Parallel in Time Stable Bi-Conjugate Gradient Algorithm},
  author = {Mohamed Kamel Riahi},
  journal= {arXiv preprint arXiv:2203.10148},
  year   = {2022}
}
R2 v1 2026-06-24T10:18:48.487Z