Dr. Bankim Chandra Mandal is an Associate Professor in the School of Basic Sciences (Mathematics). His research is centered on Numerical Analysis, Scientific Computing, and Domain Decomposition Methods for solving complex PDEs. He has made significant contributions to the development and analysis of Waveform Relaxation (WR) methods, which are iterative algorithms designed for parallel computing to tackle Space-time PDEs.

Education

At IIT Bhubaneswar: 2017 – Present

• (B.Tech. Courses): Mathematics-I, Mathematics-II, Numerical Methods, Partial Differential Equations.
• (M.Sc. Courses): Ordinary Differential Equations, Partial Differential Equations, Optimization Techniques LAB, Numerical Linear Algebra, Numerical Solutions of ODE and PDE.
• (M.Tech. Courses): Mathematical Methods.
• (ITEP Courses): Mathematical and Quantitative Reasoning.

At Michigan State University: 2016-2017

• Calculus-II (MTH 133)

At University of Geneva: 2010-2014

• Analyse Numérique

Ph.D. Students:

1. Aniruddha Banerjee (Continuing, Joint Supervision with Prof. TVS Sekhar)
2. Rakesh Kumar Sahoo (Continuing)
3. Deeksha Tomer (Submitted, 2026)
4. Soura Sana (Completed, 2025)
5. Gobinda Garai (Completed, 2024)

M.Sc. Students:

1. Pratap Mandal (2026-2027)
2. Devank (2025-2026) – Joined Ph.D. in IIT Hyderabad
3. Kishore U (2025-2026) – Joined Ph.D. in IIT Delhi
4. Somnath Giri (2024-2025) – Joined Ph.D. in IIT Mandi
5. Diya Saha (2022-2023) – Joined Ph.D. in IIT Kharagpur
6. Minakshi Verma (2022-2023) – Joined Ph.D. in Max Planck Magdeburg, Germany
7. Shivansh Bharadwaj (2021-2022)
8. Subhadeep Banik (2021-2022) – Joined TCS
9. Javed Khan (2020-2021) – Joined Akash Institute
10. Sanjana Verma (2020-2021) – Completed Ph.D. from Eindhoven University of Technology, Netherlands
11. Deepika (2019-2020)- Joined Allen
12. Nancy (2019-2020) – Joined TCS
13. Mukesh Yadav (2018-2019)
14. Animesh Pal (2018-2019) – Joined EXL Services
15. Mayank Gautam (2018-2019)
16. Jayant Sarkar (2018-2019) – Joined Galgotias University as an Assistant Professor
17. Rajesh Meena (2017-2018) – Joined Govt. Service
18. Piyush Shukla (2017-2018) – Joined Govt. Service

B.Tech. Student:

1. Arth Sojitra (2020-2021) – Joined Ph.D. in University of Tennessee Knoxville, USA

Intern Students:

1. Altaf Ahmed (2021) – Joined DevRev
2. Anan Saha (2022) – Joined Ph.D. in Louisiana State University, USA

Journal Articles:

1. Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Algorithms for Parabolic Problems; with M. Gander and F. Kwok, Electronic Transactions on Numerical Analysis, Vol. 45, 2016.
2. Neumann-Neumann Waveform Relaxation Algorithm in Multiple Subdomains for Hyperbolic Problems in 1D and 2D; Numerical Methods for Partial Differential Equations, Vol. 33(2), 2017.
3. Pipeline Implementations of Neumann-Neumann and Dirichlet-Neumann Waveform Relaxation Methods; with BW Ong, Numerical Algorithms, Vol. 78(1), 2018.
4. Dirichlet–Neumann waveform relaxation methods for parabolic and hyperbolic problems in multiple subdomains; with M. Gander and F. Kwok, BIT Numerical Mathematics, Vol. 61, 2021.
5. Convergence of substructuring methods for the Cahn–Hilliard equation; with G. Garai, Communications in Nonlinear Science and Numerical Simulation, Vol. 120, 2023.
6. Dirichlet–Neumann and Neumann-Neumann Waveform Relaxation Algorithms for Heterogeneous Sub-diffusion and Diffusion-wave Equations; with S. Sana, Computers & Mathematics with Applications, 2023.
7. Linear and Nonlinear Dirichlet-Neumann Method in Multiple Subdomains for the Cahn-Hilliard Equation; with G. Garai, International Journal of Computer Mathematics, 2023.
8. Diagonalization Based Parallel-in-Time Method for a Class of Fourth Order Time Dependent PDEs; with G. Garai, Mathematics and Computers in Simulation, https://doi.org/10.1016/j.matcom.2023.07.028, 2024.
9. On the Convergence of Overlapping and Non-overlapping Schwarz Methods for the Cahn-Hilliard Equation; with G. Garai, J. Comput. Sci., 2023.
10. Integrating Factor Based Time Integrators for the Cahn-Hilliard Equation; with G. Garai, Mathematical Methods in the Applied Sciences, 2024.
11. On the Convergence of Linear and Nonlinear Parareal Methods for the Cahn-Hilliard Equation; with G. Garai, Communications in Nonlinear Science and Numerical Simulation, Vol. 134, 2024.
12. Convergence Analysis of the Dirichlet-Neumann Waveform Relaxation Algorithm for Time Fractional Sub-Diffusion and Diffusion-Wave Equations in Heterogeneous Media; with S. Sana, Advances in Computational Mathematics, 2024.
13. Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Methods for PDEs with Time Delay; with D. Tomer, IMA J. Appl. Math., 2025.
14. Domain Decomposition based Space-time Preconditioner for the Optimal Control Problems with Constraints Imposed by the Cahn-Hilliard Equation; with G. Garai, International Journal of Computer Mathematics, 2025.
15. Discretization Strategies for Optimal Control of the Cahn-Hilliard Equation; with G. Garai, Applicable Analysis, 2026.
16. One-level and Two-level Domain Decomposition based Preconditioners for the Cahn-Hilliard Equation; with G. Garai, Journal of Applied Mathematics and Mechanics, 2026.
17. Space-time Domain Decomposition Methods for the Cahn–Hilliard equation; with G. Garai, Calcolo, 2026.
18. Convergence of Substructuring Waveform Relaxation Algorithms for Hyperbolic PDEs with Time Delay; with D. Tomer, Computational and Applied Mathematics, 2026.

Under Review:

1. Optimal Control of a Sub-diffusion Model using Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Algorithms; with S. Sana, under Review, 2025.
2. Domain Decomposition Based Fast Solver for Laplace Equation on Complex Geometries via Rational Functions; with Kishore U., under Review, 2026.
3. Dirichlet-Neumann Waveform Relaxation Methods for Hyperbolic PDE with Time Delay in Multiple Subdomain; with D. Tomer, under Review, 2026.
4. A Space-time Domain Decomposition Method on Diffusion Problem with Time Delay with Generalized Non-Standard Finite Difference Scheme on Two-Sided Graded Meshes; with Devank and D. Tomer, under Review, 2026.

Book Chapters:

1. Convergence of Substructuring Methods for Elliptic Optimal Control Problems, with M. Gander and F. Kwok, Domain Decomposition Methods in Science and Engineering XXIV,
   LNCSE, Vol. 125, Springer-Verlag, 2018.
2. Substructuring waveform relaxation methods for parabolic optimal control problems; AISC, Vol. 817, Springer, 2019.
3. Convergence of Substructuring Domain Decomposition Methods for Hamilton–Jacobi Equation; Trends in Mathematics, Birkhäuser, 2021.
4. Graded mesh in Optimal Control of Subdiffusive models and its significance in Neumann-Neumann Waveform Relaxation Algorithm; with S. Sana, Domain Decomposition Methods in Science and Engineering XXIX, LNCSE, Springer-Verlag, 2026.
5. Domain Decomposition Based Waveform Relaxation Methods for Hyperbolic Problems; with D. Tomer, Multiscale Problems: Recent Advancements in Numerical Analysis and
   Scientific Machine Learning, Springer, 2026.

Conference Proceedings:

1. A Time-Dependent Dirichlet-Neumann Method for the Heat Equation, Domain Decomposition Methods in Science and Engineering XXI, LNCSE, Vol. 98, Springer-Verlag, 2014.
2. Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation for the Wave Equation; with M. Gander and F. Kwok, Domain Decomposition Methods in Science and Engineering XXII, LNCSE, Vol. 104, Springer-Verlag, 2015.
3. Substructuring Waveform Relaxation Methods with Time Dependent Relaxation Parameter; with S. Sana, AISC, Springer, Vol. 1262, 2021.
4. Parareal Algorithms for the Cahn-Hilliard Equation; with G. Garai, Domain Decomposition Methods in Science and Engineering XXVII, LNCSE, Springer-Verlag, 2023.
5. Convergence of Neumann-Neumann Waveform Relaxation Algorithm with Time-dependent Relaxation Parameter for Time fractional Sub-diffusion and Diffusion-wave Problems; with S. Sana, Domain Decomposition Methods in Science and Engineering XXVIII, LNCSE, Springer-Verlag, 2025.
6. Convergence of Dirichlet-Neumann Waveform Relaxation Algorithm for PDEs with Time-delay in Multiple Subdomains; with D. Tomer, Domain Decomposition Methods in Science
   and Engineering XXIX, LNCSE, Springer-Verlag, 2026.

Invited Talks and Seminar:

• Talk: DNWR for the time Dependent Heat Equation; April ’12, Swiss Numerical Colloquium, Bern, Switzerland.
• Talk: DNWR for the time Dependent Heat Equation; June ’12, 21st International Domain Decomposition Methods Conference, INRIA, Rennes, France.
• Talk: DNWR for the Time-Dependent Problems; September 1-6 ’13, Domain Decomposition Methods for Optimization with PDE Constraints, Ascona, Switzerland
• Talk: Substructuring Waveform Relaxation Methods for the Wave Equation; September 16-20 ’13, 22nd International Domain Decomposition Methods Conference, USI, Lugano,
  Switzerland.
• Talk: Convergence of Substructuring Methods for Optimal Control Problems with PDE Constraints; April ’14, Swiss Numerical Colloquium, Zurich, Switzerland.
• Talk: Convergence Behavior of DNWR and NNWR methods for Space-time PDEs and Their Application to Optimal Control Problems; April ’15, Applied Mathematics Seminar, Michigan Technological University, USA.
• Invited Talk: Domain Decomposition Methods for Hamilton-Jacobi Equations; October ’15, Applied Mathematics Seminar, Department of Mathematical Sciences, Michigan State University, USA.
• Talk: Domain Decomposition methods for Optimal Control Problems, December ’17, SocProS 2017, IIT Bhubaneswar.
• Invited Talk: Convergence of Substructuring Waveform Relaxation Methods for Multiple Subdomains and Their Numerical Treatment; August ’18, International Workshop on High Performance Numerical Methods for PDEs, Northeast Normal University, China.
• Talk: Convergence of Substructuring Domain Decomposition Methods for Hamilton Jacobi Equation, February ’20, M3HPCST, Inderprastha Engineering College, New Delhi.
• Invited Talk: Substructuring-based Methods for Elliptic and Parabolic Optimal Control Problems; September ’22, Research School on Domain Decomposition for Optimal Control Problems, CIRM, Marseille, France.
• Invited Talk: Domain Decomposition Methods for Linearized and Non-Linear Cahn-Hilliard Equation; December ’23, Ramanujan Math. Soc. Conference, IIT Guwahati.
• Talk: Solving Optimal Control Problems with Cahn-Hilliard as Constraint using DD-based Preconditioners; February ’24, 28th International DDM Conference, KAUST, Saudi Arabia.
• Invited Talks: Trends in Numerical Linear Algebra; November ’24, IMA Silver Jubilee Workshop, Bhubaneswar.
• Talk: Optimal Control Problems with Diffusion-wave Equation as Constraint; June ’25, 29th International DDM Conference, Milan, Italy.
• Talk: Domain Decomposition Methods for PDEs with Time Delay; June ’25, 29th International DDM Conference, Milan, Italy.
• Invited Talk: Domain Decomposition Methods for Time Fraction PDEs; August ’25, AMSE Conference, SOA University.