| Bhatt A (2021), "Projected exponential Runge--Kutta methods for preserving dissipative properties of perturbed constrained Hamiltonian systems", Journal of Computational and Applied Mathematics. |
BibTeX:
@article{Bhatt2021,
author = {Bhatt, Ashish},
title = {Projected exponential Runge--Kutta methods for preserving dissipative properties of perturbed constrained Hamiltonian systems},
journal = {Journal of Computational and Applied Mathematics},
year = {2021},
doi = {10.1016/j.cam.2021.113556}
}
|
| Buchfink P, Bhatt A and Haasdonk B (2019), "Symplectic Model Order Reduction with Non-Orthonormal Bases", Mathematical and Computational Applications., In Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics, Bad Herrenalb, Germany. Vol. 24(2) MDPI. |
| Abstract: Parametric high-fidelity simulations are of interest for a wide range of applications. However, the restriction of computational resources renders such models to be inapplicable in a real-time context or in multi-query scenarios. Model order reduction (MOR) is used to tackle this issue. Recently, MOR is extended to preserve specific structures of the model throughout the reduction, e.g., structure-preserving MOR for Hamiltonian systems. This is referred to as symplectic MOR. It is based on the classical projection-based MOR and uses a symplectic reduced order basis (ROB). Such an ROB can be derived in a data-driven manner with the Proper Symplectic Decomposition (PSD) in the form of a minimization problem. Due to the strong nonlinearity of the minimization problem, it is unclear how to efficiently find a global optimum. In our paper, we show that current solution procedures almost exclusively yield suboptimal solutions by restricting to orthonormal ROBs. As a new methodological contribution, we propose a new method which eliminates this restriction by generating non-orthonormal ROBs. In the numerical experiments, we examine the different techniques for a classical linear elasticity problem and observe that the non-orthonormal technique proposed in this paper shows superior results with respect to the error introduced by the reduction. |
BibTeX:
@inproceedings{Buchfink2019,
author = {Buchfink, Patrick and Bhatt, Ashish and Haasdonk, Bernard},
editor = {Fritzen, Felix and Ryckelynck, David},
title = {Symplectic Model Order Reduction with Non-Orthonormal Bases},
booktitle = {Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics, Bad Herrenalb, Germany},
journal = {Mathematical and Computational Applications},
publisher = {MDPI},
year = {2019},
volume = {24},
number = {2},
url = {http://www.mdpi.com/2297-8747/24/2/43},
doi = {10.3390/mca24020043}
}
|
| Bhatt A and Moore BE (2019), "Exponential integrators preserving local conservation laws of PDEs with time-dependent damping/driving forces", Journal of Computational and Applied Mathematics. Vol. 352, pp. 341-351. |
BibTeX:
@article{Bhatt2019,
author = {Bhatt, Ashish and Moore, Brian E},
title = {Exponential integrators preserving local conservation laws of PDEs with time-dependent damping/driving forces},
journal = {Journal of Computational and Applied Mathematics},
year = {2019},
volume = {352},
pages = {341--351},
doi = {10.1016/j.cam.2018.12.003}
}
|
| Bhatt A, Fehr J and Haasdonk B (2019), "Model Order Reduction of an Elastic Body under Large Rigid Motion", In Numerical Mathematics and Advanced Applications ENUMATH, Voss, Norway. , pp. 269-277. Springer International Publishing. |
BibTeX:
@inproceedings{Bhatt2018,
author = {Bhatt, Ashish and Fehr, J. and Haasdonk, B.},
editor = {Radu, Florin Adrian and Kumar, Kundan and Berre, Inga and Nordbotten, Jan Martin and Pop, Iuliu Sorin},
title = {Model Order Reduction of an Elastic Body under Large Rigid Motion},
booktitle = {Numerical Mathematics and Advanced Applications ENUMATH, Voss, Norway},
publisher = {Springer International Publishing},
year = {2019},
pages = {269--277},
doi = {10.1007/978-3-319-96415-7_23}
}
|
| Fehr J, Grunert D, Bhatt A and Haasdonk B (2018), "Error Estimation for the Simulation of Elastic Multibody Systems", PAMM., In 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Vienna, Austria. Vol. 18(1), pp. e201800275. Wiley Online Library. |
BibTeX:
@inproceedings{Fehr2018a,
author = {Fehr, Jörg and Grunert, Dennis and Bhatt, Ashish and Haasdonk, Bernard},
title = {Error Estimation for the Simulation of Elastic Multibody Systems},
booktitle = {89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Vienna, Austria},
journal = {PAMM},
publisher = {Wiley Online Library},
year = {2018},
volume = {18},
number = {1},
pages = {e201800275},
doi = {10.1002/pamm.201800275}
}
|
| Fehr J, Grunert D, Bhatt A and Haasdonk B (2018), "A Sensitivity Study of Error Estimation in Reduced Elastic Multibody Systems", IFAC-PapersOnLine., In 9th International Conference on Mathematical Modelling, Vienna, Austria. Vol. 51(2), pp. 202-207. Elsevier. |
BibTeX:
@inproceedings{Fehr2018,
author = {Fehr, J. and Grunert, D. and Bhatt, Ashish and Haasdonk, B.},
editor = {Felix Breitenecker and Wolfgang Kemmetmüller and Andreas Körner and Andreas Kugi and Inge Troch},
title = {A Sensitivity Study of Error Estimation in Reduced Elastic Multibody Systems},
booktitle = {9th International Conference on Mathematical Modelling, Vienna, Austria},
journal = {IFAC-PapersOnLine},
publisher = {Elsevier},
year = {2018},
volume = {51},
number = {2},
pages = {202--207},
url = {http://www.sciencedirect.com/science/article/pii/S2405896318300399},
doi = {10.1016/j.ifacol.2018.03.035}
}
|
| Bhatt A and Van Gorder RA (2018), "Chaos in a non-autonomous nonlinear system describing asymmetric water wheels", Nonlinear Dynamics. Vol. 93(4), pp. 1977-1988. |
BibTeX:
@article{Bhatt2017,
author = {Bhatt, Ashish and Van Gorder, Robert A},
title = {Chaos in a non-autonomous nonlinear system describing asymmetric water wheels},
journal = {Nonlinear Dynamics},
year = {2018},
volume = {93},
number = {4},
pages = {1977--1988},
doi = {10.1007/s11071-018-4301-3}
}
|
| Bhatt A, Fehr J, Grunert D and Haasdonk B (2018), "A Posteriori Error Estimation in Model Order Reduction of Elastic Multibody Systems with Large Rigid Motion", In IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany. Springer International Publishing AG.
[BibTeX] |
BibTeX:
@inproceedings{Bhatt2018a,
author = {Bhatt, Ashish and Fehr, J. and Grunert, D. and Haasdonk, B.},
editor = {Fehr, J. and Haasdonk, B.},
title = {A Posteriori Error Estimation in Model Order Reduction of Elastic Multibody Systems with Large Rigid Motion},
booktitle = {IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany},
publisher = {Springer International Publishing AG},
year = {2018}
}
|
| Afkham BM, Bhatt A, Haasdonk B and Hesthaven JS (2018), "Symplectic Model-Reduction with a Weighted Inner Product"
[BibTeX] |
BibTeX:
@unpublished{Afkham2018,
author = {Babak Maboudi Afkham and Ashish Bhatt and Bernard Haasdonk and Jan S. Hesthaven},
title = {Symplectic Model-Reduction with a Weighted Inner Product},
year = {2018},
note = {arXiv preprint arXiv:1803.07799}
}
|
| Bhatt A and Moore BE (2016), "Structure-preserving Exponential Runge--Kutta Methods", SIAM J. Sci Comp. Vol. 39(2), pp. A593-A612. |
BibTeX:
@article{Bhatt2016,
author = {Bhatt, Ashish and Moore, B. E.},
title = {Structure-preserving Exponential Runge--Kutta Methods},
journal = {SIAM J. Sci Comp},
year = {2016},
volume = {39},
number = {2},
pages = {A593-A612},
doi = {10.1137/16m1071171}
}
|
| Bhatt A (2016), "Structure-preserving Finite Difference Methods for Linearly Damped Differential Equations". Thesis at: University of Central Florida. |
BibTeX:
@phdthesis{Bhatt2016a,
author = {Bhatt, Ashish},
title = {Structure-preserving Finite Difference Methods for Linearly Damped Differential Equations},
school = {University of Central Florida},
year = {2016},
url = {http://purl.fcla.edu/fcla/etd/CFE0006832}
}
|
| Oztepe GS, Choudhury SR and Bhatt A (2015), "Multiple Scales and Energy Analysis of Coupled Rayleigh-Van der Pol Oscillators with Time-Delayed Displacement and Velocity Feedback: Hopf Bifurcations and Amplitude Death", Far East Journal of Dynamical Systems. Vol. 26(1), pp. 31-41. |
BibTeX:
@article{Oztepe2015,
author = {Oztepe, G. S. and Choudhury, S. R. and Ashish Bhatt},
title = {Multiple Scales and Energy Analysis of Coupled Rayleigh-Van der Pol Oscillators with Time-Delayed Displacement and Velocity Feedback: Hopf Bifurcations and Amplitude Death},
journal = {Far East Journal of Dynamical Systems},
year = {2015},
volume = {26},
number = {1},
pages = {31--41},
doi = {10.17654/FJDSMar2015_031_059}
}
|
| Bhatt A, Floyd D and Moore BE (2015), "Second Order Conformal Symplectic Schemes for Damped Hamiltonian Systems", Journal of Scientific Computing. Vol. 66(3), pp. 1234-1259. |
BibTeX:
@article{Bhatt2015,
author = {Bhatt, Ashish and Floyd, D. and Moore, B. E.},
title = {Second Order Conformal Symplectic Schemes for Damped Hamiltonian Systems},
journal = {Journal of Scientific Computing},
year = {2015},
volume = {66},
number = {3},
pages = {1234--1259},
doi = {10.1007/s10915-015-0062-z}
}
|