Diagonalization based Parallel-in-Time method for a class of fourth order time dependent PDEs

Gobinda Garai and Bankim C. Mandal

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 215, issue C, 21-42

Abstract: In this paper, we design, analyze and implement efficient time parallel methods for a class of fourth order time-dependent partial differential equations (PDEs), namely the biharmonic heat equation, the linearized Cahn–Hilliard (CH) equation and the nonlinear CH equation. We use a diagonalization technique on all-at-once system to develop efficient iterative time parallel methods for investigating the solution behaviour of the said equations. We present the convergence analysis of Parallel-in-Time (PinT) algorithms. We verify our findings by presenting numerical results.

Keywords: Parallel-in-Time (PinT); Diagonalization technique; Parallel computing; Convergence analysis; Fourth-order PDEs; Cahn–Hilliard equation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:215:y:2024:i:c:p:21-42

DOI: 10.1016/j.matcom.2023.07.028

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