23 citations · 39 across the 14 of their papers we have counts for
17 papers
Dirichlet-Neumann Waveform Relaxation Method for Hyperbolic PDE with Time Delay in Multiple Subdomains
Bankim Chandra Mandal, Deeksha Tomer
Hyperbolic partial differential equations (PDEs) with time delay are essential mathematical tools used to model numerous physical systems where wave propagation or oscillations dep…
Convergence of Substructuring Waveform Relaxation Algorithms for Hyperbolic PDEs with Time Delay
Bankim Chandra Mandal, Deeksha Tomer
This article investigates the application and analysis of two substructuring waveform relaxation algorithms namely Dirichlet-Neumann Waveform Relaxation (DNWR) and Neumann-Neumann…
Dirichlet-Neumann Waveform Relaxation Method with Multiple Subdomains for Reaction-Diffusion Equation with a Time Delay
Bankim C. Mandal, Deeksha Tomer
In this study, we present the numerical investigation of the Dirichlet-Neumann Waveform Relaxation (DNWR) algorithm applied to multiple subdomains for the reaction-diffusion equati…
Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Methods for PDEs with Time Delay
Deeksha Tomer, Bankim Chandra Mandal
We introduce and compare two domain decomposition based numerical methods, namely the Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation methods (DNWR and NNWR respectively)…
Optimal Control of a Sub-diffusion Model using Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Algorithms
Soura Sana, Bankim C. Mandal
This paper explores the convergence behavior of two waveform relaxation algorithms, namely the Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation algorithms, for an optimal…
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…
Dirichlet-Neumann Waveform Relaxation Algorithm for Time Fractional Diffusion Equation in Heterogeneous Media
Soura Sana, Bankim C. Mandal
In this article, we have studied the convergence behavior of the Dirichlet-Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusion wave equations in…
Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for time fractional sub-diffusion and diffusion-wave equations
Soura Sana, Bankim C. Mandal
In this article, we have studied the convergence behavior of the Dirichlet-Neumann and Neumann- Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusi…
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…
Pipeline Implementations of Neumann-Neumann and Dirichlet-Neumann Waveform Relaxation Methods
Benjamin W. Ong, Bankim C. Mandal
This paper is concerned with the reformulation of Neumann-Neumann Waveform Relaxation (NNWR) methods and Dirichlet-Neumann Waveform Relaxation (DNWR) methods, a family of parallel…
Dirichlet-Neumann Waveform Relaxation Method for the 1D and 2D Heat and Wave Equations in Multiple subdomains
Martin J. Gander, Felix Kwok, Bankim C. Mandal
We present a Waveform Relaxation (WR) version of the Dirichlet-Neumann algorithm, formulated specially for multiple subdomains splitting for general parabolic and hyperbolic proble…
Neumann-Neumann Waveform Relaxation Algorithm in Multiple subdomains for Hyperbolic Problems in 1D and 2D
Bankim C. Mandal
We present a Waveform Relaxation (WR) version of the Neumann-Neumann algorithm for the wave equation in space-time. The method is based on a non-overlapping spatial domain decompos…
Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation for the Wave Equation
Martin J. Gander, Felix Kwok, Bankim C. Mandal
We present a Waveform Relaxation (WR) version of the Dirichlet-Neumann and Neumann-Neumann algorithms for the wave equation in space time. Each method is based on a non-overlapping…
A Time-Dependent Dirichlet-Neumann Method for the Heat Equation
Bankim C. Mandal
We present a waveform relaxation version of the Dirichlet-Neumann method for parabolic problem. Like the Dirichlet-Neumann method for steady problems, the method is based on a non-…
Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Algorithms for Parabolic Problems
Martin J. Gander, Felix Kwok, Bankim C. Mandal
We present a waveform relaxation version of the Dirichlet-Neumann and Neumann-Neumann methods for parabolic problems. Like the Dirichlet-Neumann method for steady problems, the met…