7 papers
Nonlinear Parareal-Incomplete OSWR Method for the Coupled Reaction-Diffusion System: Convergence Analysis and Computational Strategies
Gobinda Garai, Nagaiah Chamakuri
This paper presents a development of a nonlinear extension of the Parareal-Incomplete Optimized Schwarz Waveform Relaxation (OSWR) method, aimed at efficiently simulating coupled r…
Exp-ParaDiag: Time-Parallel Exponential Integrators for Parabolic PDEs
Gobinda Garai, Nagaiah Chamakuri
This paper introduces Exp-ParaDiag, a novel time-parallel method that combines the strength of exponential integrators into the ParaDiag framework. We develop and analyze Exp-ParaD…
Solution of the Optimal Control Problem for the Cahn-Hilliard Equation Using Finite Difference Approximation
Gobinda Garai, Bankim C. Mandal
This paper is concerned with the designing, analyzing and implementing linear and nonlinear discretization scheme for the distributed optimal control problem (OCP) with the Cahn-Hi…
Linear and Nonlinear Parareal Methods for the Cahn-Hilliard Equation
Gobinda Garai, Bankim C. Mandal
In this paper, we propose, analyze and implement efficient time parallel methods for the Cahn-Hilliard (CH) equation. It is of great importance to develop efficient numerical metho…
Diagonalization Based Parallel-in-Time Method for a Class of Fourth Order Time Dependent PDEs
Gobinda Garai, Bankim C. Mandal
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 h…
Convergence of substructuring Methods for the Cahn-Hilliard Equation
Gobinda Garai, Bankim C. Mandal
In this paper, we formulate and study substructuring type algorithm for the Cahn-Hilliard (CH) equation, which was originally proposed to describe the phase separation phenomenon f…
Convergence of the Neumann-Neumann Method for the Cahn-Hilliard Equation
Gobinda Garai
In this paper, we analyze a substructuring type algorithm for the Cahn-Hilliard (CH) equation. Being a nonlinear equation, it is of great importance to develop efficient numerical…