Diagonalization Based Parallel-in-Time Method for a Class of Fourth Order Time Dependent PDEs

2023/04/27 by Gobinda Garai, Garai, Gobinda, Bankim C. Mandal +1
Engineering · Materials Science · Mathematics · #65N06 #65N12 #65N15 #65Y05 #65Y20 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2304.14021

openalex publication_date 2023/04/27 · openalex created_date 2023/04/30 · openalex updated_date 2026/07/28

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.

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