Dr. Mukesh Kumar

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Edited Book

• Parallel Computational Fluids Dynamics-PARALLEL 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:978-84-941686-6-6
  (with T. Kvamsdal, A. M. Kvarving, H. Holm, C. B. Jenssen, and B. Pettersen (Eds))

Ph. D. Thesis

• Parameter-Robust Numerical Methods for Singularly Perturbed Reaction-Diffusion Problems, Department of Mathematics, Indian Institute of Technology Delhi, India, July 2009. PDF

Research Publications

• S. Sumit, S. Kumar, M. Kumar, Optimal fourth-order parameter-uniform convergence of a non-monotone scheme on equidistributed meshes for singularly perturbed reaction–diffusion problems, International Journal of Computer Mathematics, Vol. 99(8), pp. 1638-1653, 2022. DOI Link

• M. Kumar, J. Singh, S. Kumar, Aakansha, A robust numerical method for a coupled system of singularly perturbed parabolic delay problems, Engineering Computations, Vol. 38(2), pp. 964-988, 2021. DOI Link

• Sumit, S. Kumar, Kuldeep, M. Kumar, A robust numerical method for a two-parameter singularly perturbed time delay parabolic problem, Computational and Applied Mathematics, Vol. 39, no. 209, 2020. DOI Link

• L. K. Balyan, A. K. Mittal, M. Kumar, M. Choube, Stability analysis and highly accurate numerical approximation of Fisher's equations using pseudospectral method, Mathematics and Computers in Simulation, Vol. 177, pp. 86-104, 2020. DOI Link

• S. Kumar, J. Singh, M. Kumar, A robust domain decomposition method for singularly perturbed parabolic reaction-diffusion systems, Journal of Mathematical Chemistry, Vol. 57, pp. 1557-1578, 2019. DOI Link

• J. Singh, S. Kumar, M. Kumar, A high order accurate overlapping domain decomposition method for singularly perturbed reaction diffusion systems, In: Dimov I., Farago I., Vulkov L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science, vol 11386. Springer, Cham. 2019. DOI Link

• T. Kvamsdal, K. M. Okstad, M. Kumar, A. M. Kvarving, K. M. Mathisen, Adaptive isogeometric methods for thin plates, In B. Skallerud and H. I. Andersson (Eds), 10 National Conference on Computational Mechanics MekIT19 (Trondheim, Norway: MekIT19), International Center for Numerical Methods in Engineering (CIMNE), pp. 237-248, 2019, ISBN: 978-84-949194-9-7.

• J. Singh, S. Kumar, M. Kumar, A domain decomposition method for solving singularly perturbed parabolic reaction-diffusion problems with time delay, Numerical Methods for Partial Differential Equations, Vol. 34(5), pp. 2849-1866, 2018. DOI Link

• V. Gupta, M. Kumar, S. Kumar, Higher order numerical approximation for time dependent singularly perturbed differential-difference convection-diffusion equations, Numerical Methods for Partial Differential Equations, Vol. 34(1), pp. 357-380, 2018. DOI Link

• 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. 1086-1156, 2017. DOI Link

• K. M. Okstad, T. Kvamsdal, M. Kumar, K. M. Mathisen, On recovery-based error estimation in isogeometric analysis of thin plate problems, Hagsberg, J. B., & Pedersen, N. L. (Eds.) (2017). Proceedings of the 30th Nordic Seminar on Computational Mechanics (NSCM-30). Kgs. Lyngby: DTU Mechanical Engineering., pp. 151-154, 2017, (with ). PDF Link

• S. Kumar, M. Kumar, A second order uniformly convergent numerical scheme for parameterized singularly perturbed delay differential problems, Numerical Algorithms, Vol. 76(2), pp. 349-360, 2017. DOI Link

• S. Kumar, M. Kumar, Analysis of numerical methods on layer-adapted meshes for singularly perturbed quasilinear systems, Numerical Algorithms, Vol. 71(1), pp. 139-150, 2016. DOI Link

• 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. 1555-1582, 2015. DOI Link

• K. A. Johannessen, M. Kumar, T. Kvamsdal, Divergence-conforming discretization for Stokes problem on locally refined meshes using LR B-splines, Computer Methods in Applied Mechanics and Engineering, Vol. 293, pp. 38-70, 2015. DOI Link

• S. Kumar, M. Kumar,An analysis of overlapping domain decomposition methods for singularly perturbed reaction-diffusion problems, Journal of Computational and Applied Mathematics, Vol. 281, pp. 250-262, 2015. DOI Link

• T. Kvamsdal, M. Kumar, K. A. Johannessen, 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. 97-101, 2015. PDF Link

• S. Kumar, M. Kumar, High order parameter-uniform discretization for singularly perturbed parabolic partial differential equations with time delay, Computers and Mathematics with Applications, Vol. 68(10), pp. 1355-1367, 2014. DOI Link

• S. C. S. Rao, M. Kumar, An almost fourth order parameter-robust numerical method for a linear system of (M>=2) coupled singularly perturbed reaction-diffusion problems, International Journal of Numerical Analysis and Modeling, Vol. 10(3), pp. 603-621, 2013. DOI Link

• A. Buffa, D. Cho, M. Kumar, Characterization of T-splines with reduced continuity order on T-meshes, Computer Methods in Applied Mechanics and Engineering, Vol. 201-204, pp. 112-126, 2012. DOI Link

• M. Kumar, S. Kumar, High order robust approximations for singularly perturbed semilinear systems, Applied Mathematical Modeling, Vol. 36(8), pp. 3570-3579, 2012. DOI Link

• S. Kumar, M. Kumar, Parameter-robust numerical method for a system of singularly perturbed initial value problems, Numerical Algorithms, Vol. 59(2), pp. 185-195, 2012. DOI Link

• T. Kvamsdal, M. Kumar, K. A. Johannessen, and 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. 99-102, 2012, Media-Tryck Lund University, Sweden. PDF Link

• M. Kumar, T. Kvamsdal, Isogeometric collocation method with reduced continuity order NURBS and T-splines, Proceedings of the 25th Nordic Seminar on Computational Mechanics, K. Perssan, J. Revstedt, G. Sandberg, M. Wallin (Eds.), pp. 115-118, 2012, Media-Tryck Lund University, Sweden. PDF Link

• S. C. S. Rao, S. Kumar, M. Kumar, Uniform global convergence of a hybrid scheme for singularly perturbed reaction-diffusion systems, Journal of Optimization Theory and Applications, Vol. 151(2), pp. 338-352, 2011. DOI Link

• S. C. S. Rao, S. Kumar, M. Kumar, A parameter-uniform B-spline collocation method for singularly perturbed semilinear reaction-diffusion problems, Journal of Optimization Theory and Applications, Vol. 146(3), pp. 795-809, 2010. DOI Link

• M. Kumar, S. C. S. Rao, High order parameter-robust numerical method for time dependent singularly perturbed reaction-diffusion problems, Computing, Vol. 90(1)2, pp. 15-38, 2010. DOI Link

• S. C. S. Rao, M. Kumar,A uniformly convergent exponential spline difference scheme for singularly perturbed reaction-diffusion problems, Neural, Parallel and Scientific Computations, Vol. 18(2), pp. 121-135, 2010. DOI Link

• M. Kumar, S. C. S. Rao, High order parameter-robust numerical method for singularly perturbed reaction-diffusion problems, Applied Mathematics and Computation, Vol. 216(4), pp. 1036-1046, 2010. DOI Link

• S. C. S. Rao, M. Kumar, Parameter-uniformly convergent exponential spline difference scheme for singularly perturbed semilinear reaction-diffusion problems, Nonlinear Analysis: Theory, Methods and Applications, Vol. 71(12), pp. e1578-1588-1046, 2009. DOI Link

• S. C. S. Rao, M. Kumar, Parameter-uniformly convergent hybrid scheme for singularly perturbed boundary-value problems, Dynamic Systems and Applications, Vol. 5, pp. 420-424, 2008. DOI Link

• S. C. S. Rao, M. Kumar,Exponential B-spline collocation method for self-adjoint singularly perturbed boundary value problems, Applied Numerical Mathematics, Vol. 58(10), pp. 1572-1581, 2008. DOI Link

• S. C. S. Rao, M. Kumar,B-spline collocation method for nonlinear singularly-perturbed two-point boundary-value problems, Journal of Optimization Theory and Applications, Vol. 134(1), pp. 91-105, 2007. DOI Link

• S. C. S. Rao, M. Kumar,Optimal B-spline collocation method for self-adjoint singularly perturbed boundary value problems, Applied Mathematics and Computation, Vol. 188(1), pp. 749-761, 2007. DOI Link