Edited Book

Parallel Computational Fluids DynamicsPARALLEL CFD 2014
A book of extended abstracts of the 26th International Conference on Computational Fluid Dynamics held in Trondheim, Norway, May 2014, CIMNE publisher, Barcelona, Spain, ISBN:9788494168666(with T. Kvamsdal, A. M. Kvarving, H. Holm, C. B. Jenssen, and B. Pettersen (Eds))
Scientific Articles in Journals (peerreviewed)

[24] J. Singh, S. Kumar, M. Kumar, A domain decomposition method for solving singularly perturbed parabolic reactiondiffusion problems with time delay, Numerical Methods for Partial Differential Equations, 2018, In Press. http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)10982426/earlyview

[23] V. Gupta, M. Kumar, S. Kumar, Higher order numerical approximation for time dependent singularly perturbed differentialdifference convectiondiffusion equations, Numerical Methods for Partial Differential Equations, Vol. 34(1), pp. 357380, 2018, In Press. http://onlinelibrary.wiley.com/doi/10.1002/num.22203/abstract

[22] M. Kumar, T. Kvamsdal, K. A. Johannessen, Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, Vol. 316, pp. 10861156, 2017. https://doi.org/10.1016/j.cma.2016.11.014

[21] S. Kumar, M. Kumar, A second order uniformly convergent numerical scheme for parameterized singularly perturbed delay differential problems, Numerical Algorithms, Vol. 76(2), pp. 349360, 2017. http://link.springer.com/journal/11075

[20] M. Kumar, T. Kvamsdal, K. A. Johannessen, Simple a posteriori error estimators in adaptive isogeometric analysis, Computers and Mathematics with Applications, Vol. 17(7), pp. 15551582, 2015. doi:10.1016/j.camwa.2015.05.031

[19] K. A. Johannessen, M. Kumar, T. Kvamsdal, Divergenceconforming discretization for Stokes problem on locally refined meshes using LR Bsplines, Computer Methods in Applied Mechanics and Engineering, Vol. 293, pp. 3870, 2015. doi:10.1016/j.cma.2015.03.028

[18] S. Kumar, M. Kumar, Analysis of numerical methods on layeradapted meshes for singularly perturbed quasilinear systems, Numerical Algorithms, Vol. 71(1), pp. 139150, 2015. doi:10.1007/s1107501599892

[17] S. Kumar, M. Kumar, An analysis of overlapping domain decomposition methods for singularly perturbed reactiondiffusion problems, Journal of Computational and Applied Mathematics, Vol. 281, pp. 250262, 2015. PDF

[16] S. Kumar, M. Kumar, High order parameteruniform discretization for singularly perturbed parabolic partial differential equations with time delay, Computers and Mathematics with Applications, Vol. 68(10), pp. 13551367, 2014. PDF

[15] S. C. S. Rao, M. Kumar, High order parameterrobust numerical method for 2D time dependent singularly perturbed reactiondiffusion problems, International Journal of Numerical Analysis and Modeling, 2013. PDF

[14] S. C. S. Rao, M. Kumar, An almost fourth order parameterrobust numerical method for a linear system of (M>=2) coupled singularly perturbed reactiondiffusion problems, International Journal of Numerical Analysis and Modeling, Vol. 10(3), pp. 603621, 2013. PDF

[13] S. Kumar, M. Kumar, High order robust approximations for singularly perturbed semilinear systems, Applied Mathematical Modeling, Vol. 36(8), pp. 35703579, 2012. PDF

[12] S. Kumar, M. Kumar, Parameterrobust numerical method for a system of singularly perturbed initial value problems, Numerical Algorithms, Vol. 59(2), pp. 185195, 2012. PDF

[11] A. Buffa, D. Cho, M. Kumar, Characterization of Tsplines with reduced continuity order on Tmeshes, Computer Methods in Applied Mechanics and Engineering, Vol. 201204, pp. 112126, 2012. PDF

[10] S. C. S. Rao, S. Kumar, M. Kumar, Uniform global convergence of a hybrid scheme for singularly perturbed reactiondiffusion systems, Journal of Optimization Theory and Applications, Vol. 151(2), pp. 338352, 2011. PDF

[9] S. C. S. Rao, S. Kumar, M. Kumar, A parameteruniform Bspline collocation method for singularly perturbed semilinear reactiondiffusion problems, Journal of Optimization Theory and Applications, Vol. 146(3), pp. 795809, 2010. PDF

[8] M. Kumar, S. C. S. Rao, High order parameterrobust numerical method for time dependent singularly perturbed reactiondiffusion problems, Computing, Vol. 90(1)2, pp. 1538, 2010. PDF

[7] S. C. S. Rao, M. Kumar, A uniformly convergent exponential spline difference scheme for singularly perturbed reactiondiffusion problems, Neural, Parallel and Scientific Computations, Vol. 18(2), pp. 121135, 2010. PDF

[6] M. Kumar, S. C. S. Rao, High order parameterrobust numerical method for singularly perturbed reactiondiffusion problems, Applied Mathematics and Computation, Vol. 216(4), pp. 10361046, 2010. PDF

[5] S. C. S. Rao, M. Kumar, Parameteruniformly convergent exponential spline difference scheme for singularly perturbed semilinear reactiondiffusion problems, Nonlinear Analysis: Theory, Methods and Applications, Vol. 71(12), pp. e157815881046, 2009. PDF

[4] S. C. S. Rao, M. Kumar, Parameteruniformly convergent hybrid scheme for singularly perturbed boundaryvalue problems, Dynamic Systems and Applications, Vol. 5, pp. 420424, 2008. PDF

[3] S. C. S. Rao, M. Kumar, Exponential Bspline collocation method for selfadjoint singularly perturbed boundary value problems, Applied Numerical Mathematics, Vol. 58(10), pp. 15721581, 2008. PDF

[2] S. C. S. Rao, M. Kumar, Bspline collocation method for nonlinear singularlyperturbed twopoint boundaryvalue problems, Journal of Optimization Theory and Applications, Vol. 134(1), pp. 91105, 2007. PDF

[1] S. C. S. Rao, M. Kumar, Optimal Bspline collocation method for selfadjoint singularly perturbed boundary value problems, Applied Mathematics and Computation, Vol. 188(1), pp. 749761, 2007. PDF
Scientific Articles in Conference Proceedings

[3] T. Kvamsdal, M. Kumar, K. A. Johansann, A Serendipity error estimator for isogeometric analysis, Proceedings of the 28th Nordic Seminar on Computational Mechanics, CENS, Institute of Cybernetics at Tallinn University of Technology, Estonia, 2015, pp. 97101, 2015. PDF

[2] T. Kvamsdal, M. Kumar, K. A. Johansann, K. M. Okstad, Recovery based approach to design a posteriori error estimators in isogeometric analysis, Proceedings of the 25th Nordic Seminar on Computational Mechanics, K. Perssan, J. Revstedt, G. Sandberg, M. Wallin (Eds.), pp. 99102, 2012, MediaTryck Lund University, Sweden. PDF

[1] M. Kumar, T. Kvamsdal, Isogeometric collocation method with reduced continuity order NURBS and Tsplines, Proceedings of the 25th Nordic Seminar on Computational Mechanics, K. Perssan, J. Revstedt, G. Sandberg, M. Wallin (Eds.), pp. 115118, 2012, MediaTryck Lund University, Sweden. PDF
Ph. D. Thesis

M. Kumar, Parameterrobust numerical methods for singularly perturbed reactiondiffusion problems, Department of Mathematics, Indian Institute of Technology Delhi, India, July 2009. PDF