Publications
Journal
- Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Methods for Parabolic Problems, M. J. Gander, Felix Kwok, B. C. Mandal, Electronic Transactions on Numerical Analysis, Vol. 45, p. 424-456, 2016. (arXiv) (e-Version).
- Neumann-Neumann Waveform Relaxation Algorithm in Multiple Subdomains for Hyperbolic Problems in 1D and 2D, B. C. Mandal, Numerical Methods for Partial Differential Equations, DOI 10.1002/num.22112, 2016 (arXiv) (e-Version).
- Pipeline Implementations of Neumann-Neumann and Dirichlet-Neumann Waveform Relaxation Methods, B. C. Mandal, Benjamin Ong, Numerical Algorithms, 2017, DOI:10.1007/s11075-017-0364-3 (arXiv)(e-Version).
- Dirichlet-Neumann Waveform Relaxation Algorithm for the Heat and Wave Equations in Multiple subdomains, M. J. Gander, Felix Kwok, B. C. Mandal, BIT Numerical Mathematics (arXiv), 2021.
- Convergence of substructuring methods for the Cahn–Hilliard equation, G. Garai and B. C. Mandal, Communications in Nonlinear Science and Numerical Simulation, Vol. 120, 2023.
- Linear and Nonlinear Dirichlet-Neumann Method in Multiple Subdomains for the Cahn- Hilliard Equation, G. Garai and B. C. Mandal, International Journal of Computer Mathematics, 2023.
- Diagonalization Based Parallel-in-Time Method for a Class of Fourth Order Time Dependent PDEs, G. Garai and B. C. Mandal, Mathematics and Computers in Simulation, arXiv:2304.14021, 2023.
- On the Convergence of Overlapping and Non-overlapping Schwarz Methods for the Cahn- Hilliard Equation, G. Garai and B. C. Mandal, under Review, 2023.
- Space-time Domain Decomposition Methods for the Cahn–Hilliard equation, G. Garai and B. C. Mandal, under Review, 2023.
- Linear and Nonlinear Parareal Methods for the Cahn-Hilliard Equation, G. Garai and B. C. Mandal, under Review, arXiv:2304.14074, 2023.
- Integrating Factor Based Time Integrators for the Cahn-Hilliard Equation, G. Garai and B. C. Mandal, under Review, 2023.
- Dirichlet–Neumann and Neumann-Neumann Waveform Relaxation Algorithms for Heterogeneous Sub-diffusion and Diffusion-wave Equations, B. C. Mandal and S Sana, under Review, 2023.
- Dirichlet–Neumann Waveform Relaxation Algorithm for the Fractional Diffusion Equation in Heterogeneous Media, B. C. Mandal and S Sana, under Review, 2023.
Conference Proceedings
- A Time-Dependent Dirichlet-Neumann Method for the Heat Equation, B. C. Mandal, Domain Decomposition in Science and Engineering XXI, LNCSE, Vol. 98, Springer-Verlag 2014, DOI 10.1007/978-3-319-05789-7__44, pp. 467-475, (draft version)(e-Book).
- Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation for the Wave Equation, M. J. Gander, Felix Kwok, B. C. Mandal, Domain Decomposition in Science and Engineering XXII, LNCSE, Vol. 104, p. 501-509, Springer-Verlag 2015, DOI 10.1007/978-3-319-18827-0_47 (arXiv).
- Substructuring Waveform Relaxation Methods for time-variable relaxation parameter, B. C. Mandal, S. Sana, ICMC2020, AISC, Springer-Nature, Vol. 1262, 2021.
- Parareal Algorithms for the Cahn-Hilliard Equation, G. Garai and B. C. Mandal, Domain Decomposition
Methods in Science and Engineering XXVII, LNCSE, Springer-Verlag, 2023.
Book Chapter
- Convergence of Substructuring Methods for Elliptic Optimal Control Problems, M. J. Gander, Felix Kwok, B. C. Mandal, Domain Decomposition in Science and Engineering XXIV, LNCSE, Vol 125, Springer-Verlag, 2018.
- Substructuring waveform relaxation methods for parabolic optimal control problems; B. C. Mandal, AISC, Vol. 817, Springer, 2019.
- Convergence of Substructuring Domain Decomposition Methods for Hamilton-Jacobi Equation, B. C. Mandal, Trends in Mathematics, Birkhäuser, 2021.
Ph.D. Thesis
- The link is for my Ph.D. Thesis work on Domain Decomposition Methods for solving space-time problems in parallel at the University of Geneva, Switzerland. Download the full thesis from below:
| Thesis_Bankim.pdf |
Talks & Scientific works
- Talk : A Convergence Analysis for Dirichlet-Neumann and Neumann-Neumann Algorithms for time Dependent Heat Equation; March '12 , Numerical Analysis Seminar, University of Geneva.
- Talk : Dirichlet-Neumann Waveform Relaxation for the time Dependent Heat Equation; April '12, Swiss Numerical Colloquium, Bern, Switzerland.
- Talk : Dirichlet-Neumann Waveform Relaxation for the time Dependent Heat Equation; June '12, 21st International Domain Decomposition Methods Conference, INRIA, Rennes, France.
- Talk : Dirichlet-Neumann Method 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, Department of Mathematical Sciences, 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 : Pipelined Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Methods for Parabolic Problems; March '16, Applied Mathematics Seminar, Department of Mathematical Sciences, Michigan Technological University, USA.
- Attended Dobbiaco Summer School 2013 on Geometric Integration of ODEs and PDEs in Dobbiaco, Italy.
- Attended a workshop on Frontiers in Computing and Data Science in 2015 in Michigan State University, USA.
- Served as a referee for SIAM J. on Scientific Computing and LNCSE, Springer-Verlag.
M.Sc. Thesis
- The following files are for my M.Sc Thesis work on Admissible Solution for Hyperbolic Conservation Laws at IIT Bombay, India:
| 1st_stage.pdf |
| 2nd_stage.pdf |
- Have a look at the following file for the internship report at IIT Madras:
| sumintern_bankim.pdf |
