Diagonalization Based Parallel-in-Time Method for a Class of Fourth Order Time Dependent PDEs
Numerical Analysis
2023-04-28 v1 Numerical Analysis
Abstract
In this paper, we design, analyze and implement efficient time parallel method for a class of fourth order time-dependent partial differential equations (PDEs), namely biharmonic heat equation, linearized Cahn-Hilliard (CH) equation and the nonlinear CH equation. We use diagonalization technique on all-at-once system to develop efficient iterative time parallel methods for investigating the solution behaviour of said equations. We present the convergence analysis of Parallel-in-Time (PinT) algorithms. We verify our findings by presenting numerical results.
Cite
@article{arxiv.2304.14021,
title = {Diagonalization Based Parallel-in-Time Method for a Class of Fourth Order Time Dependent PDEs},
author = {Gobinda Garai and Bankim C. Mandal},
journal= {arXiv preprint arXiv:2304.14021},
year = {2023}
}