Balaje Kalyanaraman
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Balaje Kalyanaraman has a total of 6 co-authors. Here are the top co-authors by number of shared publications:
- Palla Danumjaya
BITS Pilani
2 shared publications Bishnu P. Lamichhane
1 shared publication- Bishnu Prasad Lamichhane
University of Newcastle
1 shared publication Luke G. Bennetts
1 shared publicationMichael H. Meylan
1 shared publication- Michael Howard Meylan
University of Newcastle
1 shared publication
Latest Publications
- 19 March 2022
- Published by Springer Nature in The Journal of Analysis
- Vol. 30 (4) , 1407-1426
Discontinuous Galerkin finite element methods for one-dimensional Rosenau equation
- 19 March 2022
- Published by Springer Nature in The Journal of Analysis
- Vol. 30 (4) , 1407-1426
Discontinuous Galerkin finite element methods for one-dimensional Rosenau equation
- Open Access
- 30 March 2021
- Published by The Open Journal in Journal of Open Source Software
- Vol. 6 (59) , 2939
iceFEM: A FreeFem package for wave induced ice-shelf vibrations
- 30 March 2021
- Published by The Open Journal in Journal of Open Source Software
- Vol. 6 (59) , 2939
Open AccessiceFEM: A FreeFem package for wave induced ice-shelf vibrations
- Open Access
On the Penalty term for the Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
In this paper, we present a study on the effect of penalty term in the mixed Discontinuous Galerkin Finite Element Method for the biharmonic equation proposed by \cite{gudi2008mixed}. The proposed mixed Discontinuous Galerkin Method showed sub-optimal rates of convergence for piecewise quadratic elements and no significant convergence rates for piecewise linear elements. We show that by choosing the penalty term proportional to $|e_k|^{-1}$ instead of $|e_k|^{-3}$, ensures an optimal rate of convergence for the approximation, including for piecewise linear elements. Finally, we present numerical experiments to validate our theoretical results.Open AccessOn the Penalty term for the Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
In this paper, we present a study on the effect of penalty term in the mixed Discontinuous Galerkin Finite Element Method for the biharmonic equation proposed by \cite{gudi2008mixed}. The proposed mixed Discontinuous Galerkin Method showed sub-optimal rates of convergence for piecewise quadratic elements and no significant convergence rates for piecewise linear elements. We show that by choosing the penalty term proportional to $|e_k|^{-1}$ instead of $|e_k|^{-3}$, ensures an optimal rate of convergence for the approximation, including for piecewise linear elements. Finally, we present numerical experiments to validate our theoretical results. - Open Access
- 11 October 2019
- Published by Australian Mathematical Publishing Association, Inc. in The ANZIAM Journal
- Vol. 60, C201-C214
A gradient recovery method based on an oblique projection for the virtual element method
The virtual element method is an extension of the finite element method on polygonal meshes. The virtual element basis functions are generally unknown inside an element and suitable projections of the basis functions onto polynomial spaces are used to construct the elemental stiffness and mass matrices. We present a gradient recovery method based on an oblique projection, where the gradient of the L2-polynomial projection of a solution is projected onto a virtual element space. This results in a computationally efficient numerical method. We present numerical results computing the gradients on different polygonal meshes to demonstrate the flexibility of the method. References B. Ahmad, A. Alsaedi, F. Brezzi, L. D. Marini, and A. Russo. Equivalent projectors for virtual element methods. Comput. Math. Appl., 66(3):376391, 2013. doi:10.1016/j.camwa.2013.05.015. L. Beirao da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini, and A. Russo. Basic principles of virtual element methods. Math. Mod. Meth. Appl. Sci., 23(01): 199214, 2013. doi:10.1142/S0218202512500492. L. Beirao da Veiga, F. Brezzi, L. D. Marini, and A. Russo. The hitchhiker's guide to the virtual element method. Math. Mod. Meth. Appl. Sci., 24(08): 15411573, 2014. doi:10.1142/S021820251440003X. Ilyas, M. and Lamichhane, B. P. and Meylan, M. H. A gradient recovery method based on an oblique projection and boundary modification. In Proceedings of the 18th Biennial Computational Techniques and Applications Conference, CTAC-2016, volume 58 of ANZIAM J., pages C34C45, 2017. doi:10.21914/anziamj.v58i0.11730. B. P. Lamichhane. A gradient recovery operator based on an oblique projection. Electron. Trans. Numer. Anal., 37:166172, 2010. URL http://etna.mcs.kent.edu/volumes/2001-2010/vol37/php?vol=37&pages=166-172. O. J. Sutton. Virtual element methods. PhD thesis, University of Leicester, Department of Mathematics, 2017. URL http://hdl.handle.net/2381/39955. C. Talischi, G. H. Paulino, A. Pereira, and I. F. M. Menezes. Polymesher: a general-purpose mesh generator for polygonal elements written in matlab. Struct. Multidiscip. O., 45(3):309328, 2012. doi:10.1007/s00158-011-0706-z. G. Vacca and L. Beirao da Veiga. Virtual element methods for parabolic problems on polygonal meshes. Numer. Meth. Part. D. E., 31(6): 21102134, 2015. doi:10.1002/num.21982. J. Xu and Z. Zhang. Analysis of recovery type a posteriori error estimators for mildly structured grids. Math. Comput., 73:11391152, 2004. doi:10.1090/S0025-5718-03-01600-4.
- 11 October 2019
- Published by Australian Mathematical Publishing Association, Inc. in The ANZIAM Journal
- Vol. 60, C201-C214
Open AccessA gradient recovery method based on an oblique projection for the virtual element method
The virtual element method is an extension of the finite element method on polygonal meshes. The virtual element basis functions are generally unknown inside an element and suitable projections of the basis functions onto polynomial spaces are used to construct the elemental stiffness and mass matrices. We present a gradient recovery method based on an oblique projection, where the gradient of the L2-polynomial projection of a solution is projected onto a virtual element space. This results in a computationally efficient numerical method. We present numerical results computing the gradients on different polygonal meshes to demonstrate the flexibility of the method. References B. Ahmad, A. Alsaedi, F. Brezzi, L. D. Marini, and A. Russo. Equivalent projectors for virtual element methods. Comput. Math. Appl., 66(3):376391, 2013. doi:10.1016/j.camwa.2013.05.015. L. Beirao da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini, and A. Russo. Basic principles of virtual element methods. Math. Mod. Meth. Appl. Sci., 23(01): 199214, 2013. doi:10.1142/S0218202512500492. L. Beirao da Veiga, F. Brezzi, L. D. Marini, and A. Russo. The hitchhiker's guide to the virtual element method. Math. Mod. Meth. Appl. Sci., 24(08): 15411573, 2014. doi:10.1142/S021820251440003X. Ilyas, M. and Lamichhane, B. P. and Meylan, M. H. A gradient recovery method based on an oblique projection and boundary modification. In Proceedings of the 18th Biennial Computational Techniques and Applications Conference, CTAC-2016, volume 58 of ANZIAM J., pages C34C45, 2017. doi:10.21914/anziamj.v58i0.11730. B. P. Lamichhane. A gradient recovery operator based on an oblique projection. Electron. Trans. Numer. Anal., 37:166172, 2010. URL http://etna.mcs.kent.edu/volumes/2001-2010/vol37/php?vol=37&pages=166-172. O. J. Sutton. Virtual element methods. PhD thesis, University of Leicester, Department of Mathematics, 2017. URL http://hdl.handle.net/2381/39955. C. Talischi, G. H. Paulino, A. Pereira, and I. F. M. Menezes. Polymesher: a general-purpose mesh generator for polygonal elements written in matlab. Struct. Multidiscip. O., 45(3):309328, 2012. doi:10.1007/s00158-011-0706-z. G. Vacca and L. Beirao da Veiga. Virtual element methods for parabolic problems on polygonal meshes. Numer. Meth. Part. D. E., 31(6): 21102134, 2015. doi:10.1002/num.21982. J. Xu and Z. Zhang. Analysis of recovery type a posteriori error estimators for mildly structured grids. Math. Comput., 73:11391152, 2004. doi:10.1090/S0025-5718-03-01600-4.