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Prof. Naraparaju Kishore Kumar

Associate Professor
Department of Mathematics

Numerical solutions to elliptic partial differential equations, Spectral element method, Finite element method, Tensor Decompositions
Birla Institute of Technology & Science, Pilani
Hyderabad Campus
Jawahar Nagar, Kapra Mandal
Dist.-Medchal-500 078
Telangana, India

Publications

Published

  • P. K. Dutt, N. Kishore Kumar and C. S. Upadhyay, Nonconforming h-p spectral element methods for elliptic problems, Proc. Indian Acad. Sci (Math. Sci.), Springer Verlag, 117, 109-145, 2007.
  • N. Kishore Kumar, P. K. Dutt and C. S. Upadhyay, Nonconforming spectral/hp element methods for elliptic systems, Journal of Numerical Mathematics, 17, No. 2, 119-142, 2009.
  • N. Kishore Kumar and G. Naga Raju, Least-squares hp/spectral element method for elliptic problems, Applied Numerical Mathematics, Vol. 60, 38-54,  2010. 
  • W. Hackbusch, N. Kishore Kumar and J. Schneider,  On the efficient convolution with the Newton potential, Journal of Numerical Mathematics, 18, No. 4, 257-280, 2010. Preprint: http://www.mis.mpg.de/preprints/2009/preprint2009_53.pdf
  • N. Kishore Kumar and J. Schneider, Generalized Cross approximation for 3d-tensors, Computing and Visualization in Science, 14, 105-115, 2011. Preprint: http://www.mis.mpg.de/preprints/2010/preprint2010_29.pdf
  • N. Kishore Kumar and G. Naga Raju,  Nonconforming least-squares method for elliptic partial differential equations with smooth interfaces,  Journal of Scientific Computing, 2, Vol: 53, 295-319, 2012. 
  • N. Kishore Kumar, Nonconforming spectral element method for elasticity interface problems, Journal of Applied Mathematics and Informatics,Volume 32, Issue 5-6, 761-781, 2014.
  • M. Espig, N. Kishore Kumar and J. Schneider,  A note on approximation in Tensor Chain format, Computing and Visualization in Science, Vol 5, Issue 6, 331-344, 2012.
  • G. Naga Raju, P. Dutt, N. Kishore Kumar and C. S. Upadhyay, Nonconforming spectral element method for elliptic partial differential equations with periodic boundary conditions, Applied Mathematics and Computation, Vol 246, 426-439, 2014.
  • Theeda Prasad and N. Kishore Kumar,  Image compression using pseudo--skeleton approximation, Accepted in the proceedings of   ICECCS 2013, 2013.
  • N. Kishore Kumar and Jan Schneider, Literature survey on Low rank approximation of  matrices, Accepted in Linear and Multi-linear Algebra,  Volume 65,  Issue 11, 2017.
  • Boris N. Khoromskij, Kishore K. Naraparaju and Jan Schneider, Quantized - CP approximation and sparse tensor interpolation of function generated data, Numerical Linear algebra with applications, Vol. 26(7), 2019.
  • P. Biswas, N. Kishore Kumar and Anil Kumar Kar, Performance of space-time coupled least-squares spectral element methods for parabolic problems, IOP Journal of Physics: Conference Series (JPCS), 1132, 012020, 2019.
  • P. Biswas, P. Dutt, S. Ghorai and N. Kishore Kumar , Space-time coupled least-squares spectral element methods for parabolic problems, International Journal for Computational Methods In Engineering Science and Mechanics, Vol. 20 (5), 358-371, 2019.
  • N. Kishore Kumar, Pankaj Biswas and B. Seshadri Reddy, A study of spectral element method for elliptic interface problems with nonsmooth solutions in R^2, Journal of Applied Mathematics and Informatics, Volume 38, Issue, 3-4, 311-334. 
  • N. Kishore Kumar and Pankaj Biswas, Fully discrete least-squares spectral element method for parabolic interface problems, Mathematics and Computers in Simulation 181, 364-379, 2021.
  • N. Kishore Kumar and Shubhashree Mohapatra, Nonconforming spectral element method for Oseen equations and Navier Stokes equations, In: Abdel Wahab, M. (eds) Proceedings of the 5th International Conference on Numerical Modelling in Engineering. Lecture Notes in Civil Engineering, Vol 311. Springer, Singapore. https://doi.org/10.1007/978-981-19-8429-7_1, 2023.
  • Shubhashree Mohapatra and N. Kishore Kumar, A spectral element solver for Oseen equations, To appear in ICNAAM 2021  AIP Proceedings 2849, 450036, 2023.
  • N. Kishore Kumar and Shubhashree Mohapatra, Performance of nonconforming spectral element method for Stokes problems, Computational and Applied Mathematics, 41, 156,  2022. 
  •   Shubhashree Mohapatra, N. Kishore Kumar and Shivangi Joshi, Least-squares formulations for Stokes equations with non-standard boundary conditions - A unified approach, Accepted in Mathematical Methods in Applied Sciences.
  •  N. Kishore Kumar and Shivangi Joshi, Nonconforming Spectral Element Method: A friendly introduction in one dimension and a short review in higher dimensions, Computational and Applied Mathematics, 42:139, 2023.

Submitted

  • N. Kishore Kumar, Jan Schneider, Construction of Arbitrary tensor networks using cross approximation in d=4.
  • N. Kishore Kumar and Pankaj Biswas, Fully discrete least-squares spectral element method for linear parabolic problems in R^2.
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