Hardik Kothari

Hardik Kothari

Scientific Collaborator

Publications

Submitted manuscripts

  • Integrating Multi-Preconditioned Conjugate Gradient with Additive Multigrid Strategy (2024)
    H. Kothari, M. G. C. Nestola, M. Favino, R. Krause
    [BibTeX] [Preprint] 

    @unpublished{kothari_2024a
title={Integrating Multi-Preconditioned Conjugate Gradient with Additive Multigrid Strategy}, 
author={Hardik Kothari and Maria Giuseppina Chiara Nestola and Marco Favino and Rolf Krause},
year={2024},
eprint={2402.12833},
archivePrefix={arXiv},
}

Journal articles

  • Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies (2023)
    A. Kopaničáková, H. Kothari, G. Em Karniadakis, R. Krause
    SIAM Journal on Scientific Computing (SISC)
    [Link] [BibTeX] [Preprint] 

    @article{kopanicakova_pinnspqn_2023,
 author = {Kopani\v{c}\'{a}kov\'{a}, Alena and Kothari, Hardik and Karniadakis, George E. and Krause, Rolf},
 title = {Enhancing Training of Physics-Informed Neural Networks Using Domain Decomposition–Based Preconditioning Strategies},
 journal = {SIAM Journal on Scientific Computing},
 volume = {0},
 number = {0},
 pages = {S46-S67},
 year = {2024},
 doi = {10.1137/23M1583375},
 URL = {https://doi.org/10.1137/23M1583375},
 eprint = {https://doi.org/10.1137/23M1583375},
}

  • Nonlinear field-split preconditioners for solving monolithic phase-field models of brittle fracture (2023)
    A. Kopaničáková, H. Kothari, R. Krause
    Computer Methods in Applied Mechanics and Engineering
    [Link] [BibTeX] [Preprint] 

    @article{kopanicakova_nonlinear_2023,
  title={Nonlinear field-split preconditioners for solving monolithic phase-field models of brittle fracture},
  author={Hardik Kothari and Alena Kopaničáková and Rolf Krause},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  month = {jan},
  year={2023},
  volume = {403},
  pages = {115733},
  doi = {10.1016/j.cma.2022.115733},
  url = {https://doi.org/10.1016%2Fj.cma.2022.115733},
  publisher = {Elsevier {BV}},          
}

  • A generalized multigrid method for solving contact problems in Lagrange multiplier based unfitted Finite Element method (2022)
    H. Kothari, R. Krause
    Computer Methods in Applied Mechanics and Engineering
    [Link] [BibTeX] [Preprint] 

    @article{kothari_generalized_2022,
  title = {A generalized multigrid method for solving contact problems in Lagrange multiplier based unfitted Finite Element method},
  author = {Hardik Kothari and Rolf Krause},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  month = {mar},
  year = 2022,
  volume = {392},
  pages = {114630},
  doi = {10.1016/j.cma.2022.114630},
  url = {https://doi.org/10.1016%2Fj.cma.2022.114630},
  publisher = {Elsevier {BV}},
}

  • A Multigrid Method for a Nitsche-based Extended Finite Element Method (2021)
    H. Kothari, R. Krause
    International Journal of Computing and Visualization in Science and Engineering
    [Link] [BibTeX] [Preprint] 

    @article{kothari_multigrid_2021,
  title = {A Multigrid Method for a {N}itsche-based {Extended Finite Element} Method},
  author = {Hardik Kothari and Rolf Krause},
  journal = {International Journal of Computing and Visualization in Science and Engineering},
  month = {aug},
  year = 2021,
  doi = {10.51375/ijcvse.2021.1.8},
  url = {https://doi.org/10.51375%2Fijcvse.2021.1.8},
  publisher = {G-{CSC}, University of Frankfurt},
}

Conference Proceedings

  • Nonlinear Schwarz preconditioning for Quasi-Newton methods (2024)
    H. Kothari
    Domain Decomposition Methods in Science and Engineering XXVII
    [Link] [BibTeX] [Preprint] 

    @InProceedings{kothari_raspqn_2024,
  author="Kothari, Hardik",
  editor="Dost{\'a}l, Zden{\v{e}}k
      and Kozubek, Tom{\'a}{\v{s}}
      and Klawonn, Axel
      and Langer, Ulrich
      and Pavarino, Luca F.
      and {\v{S}}{\'i}stek, Jakub
      and Widlund, Olof B.",
  title="Nonlinear Schwarz Preconditioning for Quasi-Newton Methods",
  booktitle="Domain Decomposition Methods in Science and Engineering XXVII",
  year="2024",
  publisher="Springer Nature Switzerland",
  address="Cham",
  pages="311--318",
  isbn="978-3-031-50769-4"
}

  • Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints (2024)
    H. Kothari, A. Kopaničáková, R. Krause
    Domain Decomposition Methods in Science and Engineering XXVII
    [Link] [BibTeX] [Preprint] 

    @InProceedings{kothari_raspqn_const_2024,
  author="Kothari, Hardik
      and Kopanic{\'a}kov{\'a}, Alena
      and Krause, Rolf",
  editor="Dost{\'a}l, Zden{\v{e}}k
      and Kozubek, Tom{\'a}{\v{s}}
      and Klawonn, Axel
      and Langer, Ulrich
      and Pavarino, Luca F.
      and {\v{S}}{\'i}stek, Jakub
      and Widlund, Olof B.",
  title="Nonlinear Schwarz Preconditioning for Nonlinear Optimization Problems with Bound Constraints",
  booktitle="Domain Decomposition Methods in Science and Engineering XXVII",
  year="2024",
  publisher="Springer Nature Switzerland",
  address="Cham",
  pages="319--326",
  isbn="978-3-031-50769-4"
}

  • A Multigrid Preconditioner for Jacobian-free Newton-Krylov Methods (2023)
    H. Kothari, A. Kopaničáková, R. Krause
    Domain Decomposition Methods in Science and Engineering XXVI
    [Link] [BibTeX] [Preprint] 

    @InProceedings{kothari_multigrid_2023,
  author="Kothari, Hardik
          and Kopani{\v{c}}{\'a}kov{\'a}, Alena
          and Krause, Rolf",
  editor="Brenner, Susanne C.
          and Chung, Eric
          and Klawonn, Axel
          and Kwok, Felix
          and Xu, Jinchao
          and Zou, Jun",
  title="A Multigrid Preconditioner for Jacobian-free Newton--Krylov Methods",
  booktitle="Domain Decomposition Methods in Science and Engineering XXVI",
  year="2023",
  publisher="Springer International Publishing",
  address="Cham",
  pages="365--372",
}

  • Multigrid and Saddle-Point Preconditioners for Unfitted Finite Element Modelling of Inclusions (2020)
    H. Kothari, R. Krause
    14th WCCM-ECCOMAS Congress
    [Link] [BibTeX] [Preprint] 

    @InProceedings{kothari_multigrid_2021b,
  author="Kothari, Hardik
          and Krause, Rolf",
  editor="F. Chinesta and R. Abgrall and O. Allix",
  title={Multigrid and Saddle-Point Preconditioners for Unfitted Finite Element Modelling of Inclusions},
  booktitle = {14th {WCCM}-{ECCOMAS} Congress}
  year="2021",
  doi = "10.23967/wccm-eccomas.2020.211"
  publisher = {{CIMNE},
}

Thesis