Publications

@article{antil_kouri_Pfefferer_2020,

title = {Fractional diffusion and uncertainty},

author = {H. Antil and D. P. Kouri and J. Pfefferer},

doi = {https://doi.org/10.1137/20M1324958},

year  = {2021},

date = {2021-03-29},

journal = {SIAM Journal on Control and Optimization},

volume = {59},

number = {2},

pages = {1161–1187},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_TSBrown_DVerma_MWarma_2021a,

title = {Optimal Control of Fractional PDEs with State and Control Constraints},

author = {Harbir Antil and Thomas S Brown and Deepanshu Verma and Mahamadi Warma},

year  = {2021},

date = {2021-01-01},

journal = {Pure and Applied Functional Analysis},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_PDondl_LStriet_2021a,

title = {Approximation of Integral Fractional Laplacian and Fractional PDEs via sinc-Basis},

author = {Harbir Antil and Patrick Dondl and Ludwig Striet},

year  = {2021},

date = {2021-01-01},

journal = {To appear: SIAM J. of Sci. Comp.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_HCElman_AOnwunta_DVerma_2021a,

title = {Novel Deep neural networks for solving Bayesian statistical inverse problems},

author = {Harbir Antil and Howard C Elman and Akwum Onwunta and Deepanshu Verma},

year  = {2021},

date = {2021-01-01},

journal = {arXiv preprint arXiv:2102.03974},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_DPKouri_JPfefferer_2021a,

title = {Risk-Averse Control of Fractional Điffusion with Uncertain Exponent},

author = {Harbir Antil and Drew P Kouri and Johannes Pfefferer},

url = {https://doi.org/10.1137/20M1324958},

doi = {10.1137/20M1324958},

issn = {0363-0129},

year  = {2021},

date = {2021-01-01},

journal = {SIAM J. Control Optim.},

volume = {59},

number = {2},

pages = {1161--1187},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_DPKouri_DRidzal_2021a,

title = {ALESQP: An Augmented Lagrangian Equality-constrained SQP Method for Optimization with General Constraints},

author = {Harbir Antil and Drew P Kouri and D Ridzal},

year  = {2021},

date = {2021-01-01},

journal = {Submitted to SIOPT},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{TSBrown_HAntil_RLoehner_FTogashi_DVerma_2021a,

title = {Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows},

author = {Thomas S Brown and Harbir Antil and Rainald Löhner and Fumiya Togashi and Deepanshu Verma},

year  = {2021},

date = {2021-01-01},

journal = {arXiv preprint arXiv:2104.01914},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_SBartels_ASchikorra_2021a,

title = {Approximation of fractional harmonic maps},

author = {Harbir Antil and Sören Bartels and Armin Schikorra},

year  = {2021},

date = {2021-01-01},

journal = {arXiv preprint arXiv:2104.10049},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{RLohner_HAntil_2021a,

title = {High fidelity modeling of aerosol pathogen propagation in built environments with moving pedestrians},

author = {Rainald Löhner and Harbir Antil},

year  = {2021},

date = {2021-01-01},

journal = {International Journal for Numerical Methods in Biomedical Engineering},

volume = {37},

number = {3},

pages = {e3428},

publisher = {Wiley Online Library},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HDinh_HAntil_YChen_ECherkaev_ANarayana_2019a,

title = {Model reduction for fractional elliptic problems using Kato's formula},

author = {Huy Dinh and Harbir Antil and Yanlai Chen and Elena Cherkaev and Akil Narayan},

url = {arXiv:1904.09332 

http://aimsciences.org//article/id/1d28d5fa-c41e-4127-80ef-8907c0fac247},

doi = {10.3934/mcrf.2021004},

issn = {2156-8472},

year  = {2021},

date = {2021-01-01},

journal = {Mathematical Control & Related Fields},

volume = {0},

number = {2156-8472_2021004},

abstract = {We propose a novel numerical algorithm utilizing model reduction for computing solutions to stationary partial differential equations involving the spectral fractional Laplacian. Our approach utilizes a known characterization of the solution in terms of an integral of solutions to local (classical) elliptic problems. We reformulate this integral into an expression whose continuous and discrete formulations are stable; the discrete formulations are stable independent of all discretization parameters. We subsequently apply the reduced basis method to accomplish model order reduction for the integrand. Our choice of quadrature in discretization of the integral is a global Gaussian quadrature rule that we observe is more efficient than previously proposed quadrature rules. Finally, the model reduction approach enables one to compute solutions to multi-query fractional Laplace problems with orders of magnitude less cost than a traditional solver.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MPanagoda_TBerry_HAntil_2021a,

title = {Convergence Analysis of the Rank-Restricted Soft SVD Algorithm},

author = {Mahendra Panagoda and Tyrus Berry and Harbir Antil},

year  = {2021},

date = {2021-01-01},

journal = {arXiv preprint arXiv:2104.01473},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_TBerry_JHarlim_2021a,

title = {Fractional diffusion maps},

author = {Harbir Antil and Tyrus Berry and John Harlim},

year  = {2021},

date = {2021-01-01},

journal = {Applied and Computational Harmonic Analysis},

volume = {54},

pages = {145--175},

publisher = {Elsevier},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{CGlusa_HAntil_MDElia_BWaanders_CJWeiss_2021a,

title = {A fast solver for the fractional Ħelmholtz equation},

author = {Christian Glusa and Harbir Antil and Marta D'Elia and Bart Bloemen Waanders and Chester J Weiss},

url = {https://doi.org/10.1137/19M1302351},

doi = {10.1137/19M1302351},

issn = {1064-8275},

year  = {2021},

date = {2021-01-01},

journal = {SIAM J. Sci. Comput.},

volume = {43},

number = {2},

pages = {A1362--A1388},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_CNRautenberg_ASchikorra_2021a,

title = {On a Fractional Version of a Murat Compactness Result and Applications},

author = {Harbir Antil and Carlos N Rautenberg and Armin Schikorra},

url = {https://doi.org/10.1137/20M1379873},

doi = {10.1137/20M1379873},

issn = {0036-1410},

year  = {2021},

date = {2021-01-01},

journal = {SIAM J. Math. Anal.},

volume = {53},

number = {3},

pages = {3158--3187},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_TSBrown_RLohner_FTogashi_DVerma_2021a,

title = {Deep Neural Nets with Fixed Bias Configuration},

author = {Harbir Antil and Thomas S Brown and Rainald Löhner and Fumiya Togashi and Deepanshu Verma},

year  = {2021},

date = {2021-01-01},

journal = {arXiv preprint arXiv:2107.01308},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{RLoehner_HAntil_et_al_2021a,

title = {Deep learning or interpolation for inverse modelling of heat and fluid flow problems?},

author = {Rainald Löhner and Harbir Antil and Hamid Tamaddon-Jahromi and Neeraj Kavan Chakshu and Perumal Nithiarasu},

year  = {2021},

date = {2021-01-01},

journal = {International Journal of Numerical Methods for Heat & Fluid Flow},

publisher = {Emerald Publishing Limited},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Antil_Draganescu_Green,

title = {A Note on Multigrid Preconditioning for Fractional PDE-Constrained Optimization Problems},

author = {Harbir Antil and Andrei Draganescu and Kiefer Green.},

url = {https://www.sciencedirect.com/science/article/pii/S2590037420300431},

doi = {https://doi.org/10.1016/j.rinam.2020.100133},

issn = {2590-0374},

year  = {2020},

date = {2020-12-04},

journal = {Results in Applied Mathematics},

volume = {9},

pages = {100133},

abstract = {In this note we present a multigrid preconditioning method for solving quadratic optimization problems constrained by a fractional diffusion equation. Multigrid methods within the all-at-once approach to solve the first order optimality Karush–Kuhn–Tucker (KKT) systems are widely popular, but their development have relied on the underlying systems being sparse. On the other hand, for most discretizations, the matrix representation of fractional operators is expected to be dense. We develop a preconditioning strategy for our problem based on a reduced approach, namely we eliminate the state constraint using the control-to-state map. Our multigrid preconditioning approach shows a dramatic reduction in the number of CG iterations. We assess the quality of preconditioner in terms of the spectral distance. Finally, we provide a partial theoretical analysis for this preconditioner, and we formulate a conjecture which is clearly supported by our numerical experiments.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_RKhatri_RLohner_DVerma_2020a,

title = {Fractional Deep Neural Network via Constrained Optimization},

author = {Harbir Antil and Ratna Khatri and Rainald Löhner and Deepanshu Verma},

doi = {https://doi.org/10.1088/2632-2153/aba8e7},

year  = {2020},

date = {2020-12-01},

journal = {Machine Learning: Science and Technology},

volume = {21},

number = {1},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_SKubota_KShirakawa_NYamazaki_2020a,

title = {Optimal Control Problems Governed by 1-D Kobayashi-Warren-Carter Type Systems},

author = {Harbir Antil and Shodai Kubota and Ken Shirakawa and Noriaki Yamazaki},

url = {arXiv:2003.01297},

doi = {10.3934/mcrf.2020036},

year  = {2020},

date = {2020-08-13},

journal = {Mathematical Control & Related Fields},

volume = {11},

number = {2},

pages = {253-289},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{hardesty_antil_kouri_ridzal,

title = {The Strip Method for Shape Derivatives},

author = {S. Hardesty and H. Antil and D. P. Kouri and D. Ridzal},

url = {http://www.optimization-online.org/DB_HTML/2020/08/7986.html},

year  = {2020},

date = {2020-08-07},

keywords = {},

pubstate = {forthcoming},

tppubtype = {article}

}

@article{Löhner_Antil_Idelsohn_Oñate,

title = {Detailed Simulation of Viral Propagation In The Built Environment},

author = {Rainald Löhner and Harbir Antil and Sergio Idelsohn and Eugenio Oñate},

url = {https://arxiv.org/pdf/2006.13792.pdf},

doi = {https://doi.org/10.1007/s00466-020-01881-7},

year  = {2020},

date = {2020-08-05},

journal = {Computational Mechanics},

abstract = {A summary is given of the mechanical characteristics of virus contaminants and the transmission via droplets and aerosols. The ordinary and partial differential equations describing the physics of these processes with high fidelity are presented, as well as appropriate numerical schemes to solve them. Several examples taken from recent evaluations of the built environment are shown, as well as the optimal placement of sensors.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1021/acs.jcim.0c00308,

title = {Generalizable Framework for Algorithmic Interpretation of Thin Film Morphologies in Scanning Probe Images},

author = {Wesley K Tatum and Diego Torrejon and Patrick O’Neil and Jonathan W Onorato and Anton B Resing and Sarah Holliday and Lucas Q Flagg and David S Ginger and Christine K Luscombe},

url = {https://doi.org/10.1021/acs.jcim.0c00308},

doi = {10.1021/acs.jcim.0c00308},

year  = {2020},

date = {2020-06-11},

journal = {Journal of Chemical Information and Modeling},

abstract = {We describe an open-source and widely adaptable Python library that recognizes morphological features and domains in images collected via scanning probe microscopy. π-Conjugated polymers (CPs) are ideal for evaluating the Materials Morphology Python (m2py) library because of their wide range of morphologies and feature sizes. Using thin films of nanostructured CPs, we demonstrate the functionality of a general m2py workflow. We apply numerical methods to enhance the signals collected by the scanning probe, followed by Principal Component Analysis (PCA) to reduce the dimensionality of the data. Then, a Gaussian Mixture Model segments every pixel in the image into phases, which have similar material-property signals. Finally, the phase-labeled pixels are grouped and labeled as morphological domains using either connected components labeling or persistence watershed segmentation. These tools are adaptable to any scanning probe measurement, so the labels that m2py generates will allow researchers to individually address and analyze the identified domains in the image. This level of control, allows one to describe the morphology of the system using quantitative and statistical descriptors such as the size, distribution, and shape of the domains. Such descriptors will enable researchers to quantitatively track and compare differences within and between samples.},

note = {PMID: 32526145},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_ZDi_RKhatri_2020a,

title = {Bilevel optimization, deep learning and fractional Laplacian regularizatin with applications in tomography},

author = {Harbir Antil and Zichao Wendy Di and Ratna Khatri},

url = {https://doi.org/10.1088%2F1361-6420%2Fab80d7},

doi = {10.1088/1361-6420/ab80d7},

year  = {2020},

date = {2020-05-01},

journal = {Inverse Problems},

volume = {36},

number = {6},

pages = {064001},

publisher = {IOP Publishing},

abstract = {In this work we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction quality, and compare it with the total variation regularization. We emphasize that the key advantage of using fractional Laplacian as a regularizer is that it leads to a linear operator, as opposed to the total variation regularization which results in a nonlinear degenerate operator. Inspired by residual neural networks, to learn the optimal strength of regularization and the exponent of fractional Laplacian, we develop a dedicated bilevel optimization neural network with a variable depth for a general regularized inverse problem. We illustrate how to incorporate various regularizer choices into our proposed network. As an example, we consider tomographic reconstruction as a model problem and show an improvement in reconstruction quality, especially for limited data, via fractional Laplacian regularization. We successfully learn the regularization strength and the fractional exponent via our proposed bilevel optimization neural network. We observe that the fractional Laplacian regularization outperforms total variation regularization. This is specially encouraging, and important, in the case of limited and noisy data.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{articled,

title = {Realization of the fractional Laplacian with nonlocal exterior conditions via forms method},

author = {Burkhard Claus and Mahamadi Warma},

doi = {10.1007/s00028-020-00567-0},

year  = {2020},

date = {2020-01-01},

journal = {Journal of Evolution Equations},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{WarmaNullCF,

title = {Null controllability from the exterior of a one-dimensional nonlocal heat equation},

author = {Mahamadi Warma and S Zamorano},

year  = {2020},

date = {2020-01-01},

journal = {Control & Cybernetics},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{2163-2480_2020_2_399,

title = {Null-controllability properties of a fractional wave equation with a memory term},

author = {Umberto Biccari and Mahamadi Warma},

url = {http://aimsciences.org//article/id/2e926a6a-8cf0-4294-8a42-c4a27c6ceffc},

doi = {10.3934/eect.2020011},

year  = {2020},

date = {2020-01-01},

journal = {Evolution Equations & Control Theory},

volume = {9},

number = {2163-2480_2020_2_399},

pages = {399},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{1078-0947_2020_5_2875,

title = {A Gevrey class semigroup for a thermoelastic plate model with a fractional Laplacian: Between the Euler-Bernoulli and Kirchhoff models},

author = {Valentin Keyantuo and Louis Tebou and Mahamadi Warma},

url = {http://aimsciences.org//article/id/e9d97625-0c79-4df4-b552-5facb64317ee},

doi = {10.3934/dcds.2020152},

issn = {1078-0947},

year  = {2020},

date = {2020-01-01},

journal = {Discrete & Continuous Dynamical Systems - A},

volume = {40},

number = {1078-0947_2020_5_2875},

pages = {2875},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{RLohner_HAntil_2020a,

title = {Determination of volumetric material data from boundary measurements: Revisiting Calderon's Problem},

author = {Rainald Löhner and Harbir Antil},

year  = {2020},

date = {2020-01-01},

journal = {International Journal of Numerical Methods for Heat & Fluid Flow},

publisher = {Emerald Publishing Limited},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_TTNQuyen_2020a,

title = {Optimal Control of Parameterized Maxwell's System: Reduced Basis, Convergence Analysis, and A Posteriori Error Estimates},

author = {Harbir Antil and Tran Tam Nhan Quyen},

year  = {2020},

date = {2020-01-01},

journal = {arXiv},

pages = {arXiv--1908},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{CJWeiss_BGVBWaanders_HAntil_2020a,

title = {Fractional operators applied to geophysical electromagnetics},

author = {Chester J Weiss and Bart G Bloemen Waanders and Harbir Antil},

year  = {2020},

date = {2020-01-01},

journal = {Geophysical Journal International},

volume = {220},

number = {2},

pages = {1242--1259},

publisher = {Oxford University Press},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_DVerma_MWarma_2020a,

title = {External optimal control of fractional parabolic PDEs},

author = {Harbir Antil and Deepanshu Verma and Mahamadi Warma},

url = {https://doi.org/10.1051/cocv/2020005},

doi = {10.1051/cocv/2020005},

issn = {1292-8119},

year  = {2020},

date = {2020-01-01},

journal = {ESAIM Control Optim. Calc. Var.},

volume = {26},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_MWarma_2020a,

title = {Optimal control of fractional semilinear PDEs},

author = {Harbir Antil and Mahamadi Warma},

url = {https://doi.org/10.1051/cocv/2019003},

doi = {10.1051/cocv/2019003},

issn = {1292-8119},

year  = {2020},

date = {2020-01-01},

journal = {ESAIM Control Optim. Calc. Var.},

volume = {26},

pages = {Paper No. 5, 30},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{aragones2020approximate,

title = {Approximate and mean approximate controllability properties for Hilfer time-fractional differential equations},

author = {Ernest Aragones and Valentin Keyantuo and Mahamadi Warma},

year  = {2020},

date = {2020-01-01},

journal = {arXiv preprint arXiv:2003.08188},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_MWarma_2019a,

title = {Optimal control of the coefficient for the regional fractional $p$-Laplace equation: approximation and convergence},

author = {Harbir Antil and Mahamadi Warma},

url = {https://doi.org/10.3934/mcrf.2019001},

doi = {10.3934/mcrf.2019001},

issn = {2156-8472},

year  = {2019},

date = {2019-01-01},

journal = {Math. Control Relat. Fields},

volume = {9},

number = {1},

pages = {1--38},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MR4034588,

title = {Corrigendum to: Đirichlet and Neumann boundary conditions 

 for the $p$-Laplace operator: What is in between?},

author = {Ralph Chill and Mahamadi Warma},

doi = {10.1017/prm.2018.156},

issn = {0308-2105},

year  = {2019},

date = {2019-01-01},

journal = {Proc. Roy. Soc. Edinburgh Sect. A},

volume = {149},

number = {6},

pages = {1689--1691},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MR3949124,

title = {Lattice dynamical systems associated with a fractional 

 Laplacian},

author = {Valentin Keyantuo and Carlos Lizama and Mahamadi Warma},

doi = {10.1080/01630563.2019.1602542},

issn = {0163-0563},

year  = {2019},

date = {2019-01-01},

journal = {Numer. Funct. Anal. Optim.},

volume = {40},

number = {11},

pages = {1315--1343},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MR3968237,

title = {Approximate controllability from the exterior of space-time 

 fractional diffusive equations},

author = {Mahamadi Warma},

doi = {10.1137/18M117145X},

issn = {0363-0129},

year  = {2019},

date = {2019-01-01},

journal = {SIAM J. Control Optim.},

volume = {57},

number = {3},

pages = {2037--2063},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MR3978051,

title = {Asymptotic behavior of mild solutions for a class of abstract 

 nonlinear difference equations of convolution type},

author = {Valentin Keyantuo and Carlos Lizama and Silvia Rueda and Mahamadi Warma},

doi = {10.1186/s13662-019-2189-y},

issn = {1687-1839},

year  = {2019},

date = {2019-01-01},

journal = {Adv. Difference Equ.},

pages = {Paper No. 251, 29},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MR4031765,

title = {Fractional Gaussian estimates and holomorphy of semigroups},

author = {Valentin Keyantuo and Fabian Seoanes and Mahamadi Warma},

doi = {10.1007/s00013-019-01381-y},

issn = {0003-889X},

year  = {2019},

date = {2019-01-01},

journal = {Arch. Math. (Basel)},

volume = {113},

number = {6},

pages = {629--647},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_RKhatri_MWarma_2019a,

title = {External optimal control of nonlocal PDEs},

author = {Harbir Antil and Ratna Khatri and Mahamadi Warma},

url = {https://doi.org/10.1088/1361-6420/ab1299},

doi = {10.1088/1361-6420/ab1299},

issn = {0266-5611},

year  = {2019},

date = {2019-01-01},

journal = {Inverse Problems},

volume = {35},

number = {8},

pages = {084003, 35},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_YChen_ANarayan_2019a,

title = {Reduced basis methods for fractional Laplace equations via extension},

author = {Harbir Antil and Yanlai Chen and Akil Narayan},

url = {https://doi.org/10.1137/18M1204802},

doi = {10.1137/18M1204802},

issn = {1064-8275},

year  = {2019},

date = {2019-01-01},

journal = {SIAM J. Sci. Comput.},

volume = {41},

number = {6},

pages = {A3552--A3575},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{RVaughn_TBerry_HAntil_2019a,

title = {Diffusion Maps for Embedded Manifolds with Boundary with Applications to PDEs},

author = {Ryan Vaughn and Tyrus Berry and Harbir Antil},

year  = {2019},

date = {2019-01-01},

journal = {arXiv preprint arXiv:1912.01391},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_UBiccari_RPonce_MWarma_2019a,

title = {Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation},

author = {Harbir Antil and Umberto Biccari and Rodrigo Ponce and Mahamadi Warma and Sebastián Zamorano},

year  = {2019},

date = {2019-01-01},

journal = {arXiv preprint arXiv:1910.14529},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_CLizama_RPonce_MWarma_2019a,

title = {Convergence of solutions of discrete semi-linear space-time fractional evolution equations},

author = {Harbir Antil and Carlos Lizama and Rodrigo Ponce and Mahamadi Warma},

year  = {2019},

date = {2019-01-01},

journal = {arXiv preprint arXiv:1910.07358},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ZZou_SMukherjee_HAntil_WAquino_2019a,

title = {Adaptive particle-based approximations of the Gibbs posterior for inverse problems},

author = {Zilong Zou and Sayan Mukherjee and Harbir Antil and Wilkins Aquino},

year  = {2019},

date = {2019-01-01},

journal = {arXiv preprint arXiv:1907.01551},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{AHazra_VMaggioni_PHouser_HAntil_MNoonan_2019a,

title = {A Monte Carlo-based multi-objective optimization approach to merge different precipitation estimates for land surface modeling},

author = {Abheera Hazra and Viviana Maggioni and Paul Houser and Harbir Antil and Margaret Noonan},

year  = {2019},

date = {2019-01-01},

journal = {Journal of hydrology},

volume = {570},

pages = {454--462},

publisher = {Elsevier},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HAntil_TSBrown_FJSayas_2019a,

title = {A problem in control of elastodynamics with piezoelectric effects},

author = {Harbir Antil and Thomas S Brown and Francisco-Javier Sayas},

url = {https://doi.org/10.1093/imanum/drz047},

doi = {10.1093/imanum/drz047},

issn = {0272-4979},

year  = {2019},

date = {2019-01-01},

journal = {IMA Journal of Numerical Analysis},

abstract = {We consider an optimal control problem where the state equations are a coupled hyperbolic--elliptic system. This system arises in elastodynamics with piezoelectric effects---the elastic stress tensor is a function of elastic displacement and electric potential. The electric flux acts as the control variable and bound constraints on the control are considered. We develop a complete analysis for the state equations and the control problem. The requisite regularity on the control, to show the well-posedness of the state equations, is enforced using the cost functional. We rigorously derive the first-order necessary and sufficient conditions using adjoint equations and further study their well-posedness. For spatially discrete (time-continuous) problems, we show the convergence of our numerical scheme. Three-dimensional numerical experiments are provided showing convergence properties of a fully discrete method and the practical applicability of our approach.},

note = {drz047},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1137/18M1224970,

title = {Sobolev Spaces with Non-Muckenhoupt Weights, Fractional Elliptic Operators, and Applications},

author = {Harbir Antil and Carlos N Rautenberg},

url = {https://doi.org/10.1137/18M1224970},

doi = {10.1137/18M1224970},

year  = {2019},

date = {2019-01-01},

journal = {SIAM Journal on Mathematical Analysis},

volume = {51},

number = {3},

pages = {2479-2503},

keywords = {},

pubstate = {published},

tppubtype = {article}

}