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Diagonalization Based Parallel-in-Time Method for a Class of Fourth Order Time Dependent PDEs (2304.14021v1)
Published 27 Apr 2023 in math.NA and cs.NA
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.