Harbir Antil

Articles in Review

  1. H. Antil, T. Berry, and J. Harlim.
    Fractional Diffusion Maps.
    Submitted 2018. arxiv

  2. H. Antil, Y. Chen, and A. Narayan.
    Certified reduced basis methods for fractional Laplace equations via extension.
    Submitted 2018. arxiv

  3. A. Hazra, V. Maggioni, P. Houser, H. Antil and M. Noonan.
    A monte carlo-based multi-objective optimization approach to merge different precipitation estimates for land surface modeling.
    Submitted 2018.

  4. H. Antil and C.N. Rautenberg.
    Sobolev spaces with non-Muckenhoupt weights, fractional elliptic operators, and applications.
    Submitted 2018. arxiv

  5. H. Antil, T. Brown, and F.J. Sayas.
    A problem in control of elastodynamics with piezoelectric effects.
    Submitted 2018. arxiv

  6. H. Antil and M. Warma.
    Optimal control of fractional semilinear PDEs.
    Submitted 2017. arxiv

  7. H. Antil, R. H. Nochetto, and P. Sodré.
    The Stokes problem with Navier slip boundary condition: Minimal fractional Sobolev regularity of the domain.
    Submitted 2015. arxiv
Book (accepted)
  1. H. Antil, Drew Kouri, Martin Lacasse, and Denis Ridzal.
    Frontiers in PDE-constrained Optimization.
    The IMA Volumes in Mathematics and its Applications, Springer 2018. Link

Published Articles

  1. H. Antil, K. Shirakawa, and N. Yamazaki.
    A class of parabolic systems associated with optimal control of grain boundary motions.
    Accepted in Advances in Mathematical Sciences and Applications 2018.

  2. H. Antil, J. Pfefferer, and S. Rogovs.
    Fractional operators with inhomogeneous boundary bonditions: analysis, control, and discretization.
    Accepted in Communications in Mathematical Sciences (CMS) 2018. arxiv

  3. H. Antil, R. H. Nochetto, and P. Venegas.
    Controlling the Kelvin force: Basic Strategies and Applications to Magnetic Drug Targeting.
    Accepted in Optimization and Engineering, 2018. arxiv

  4. H. Antil, D. Chen, and S. E. Field.
    A Note on QR-Based Model Reduction: Algorithm, Software, and Gravitational Wave Applications.
    Accepted in Computing in Science and Engineering 2018. arxiv

  5. H. Antil.
    PDE Constrained Optimization . 2018. Code

  6. H. Antil, E. Otarola, and A. J. Salgado.
    Optimization with respect to order in a fractional diffusion model: analysis, approximation and algorithmic aspects
    Accepted in Journal of Scientific Computing, 2018. Published version

  7. H. Antil and M. Warma.
    Optimal control of the coefficient for fractional p-Laplace equation: Approximation and convergence.
    To appear in RIMS Proceedings 2018.

  8. H. Antil and M. Warma.
    Optimal control of the coefficient for regional fractional p-Laplace equation: Approximation and convergence.
    Accepted in Mathematical Control & Related Fields 2018. arxiv

  9. H. Antil and D. Leykekhman.
    A brief introduction to PDE constrained optimization.
    Accepted in The IMA Volumes in Mathematics and its Applications, Springer (2018).

  10. H. Antil, and C. N. Rautenberg.
    Fractional elliptic quasi-variational inequalities: theory and numerics.
    Accepted in Interface and Free Boundaries 2018. arxiv

  11. H. Antil, R. H. Nochetto, and P. Venegas.
    Optimizing the Kelvin Force in a Moving Target Subdomain.
    Accepted in M3AS 2018. arxiv

  12. H. Antil, and S. W. Walker.
    Optimal Control of a Degenerate PDE for Surface Shape.
    DOI: 10.1007/s00245-017-9407-3. Appl. Math. Optim. 78 (2), 297--328, 2018 link

  13. H. Antil and J. Pfefferer.
    A short Matlab implementation of fractional Poisson equation with nonzero boundary conditions.
    Technical Report 2017. Technical Report and Code

  14. H. Antil and S. Bartels.
    Spectral approximation of fractional PDEs in image processing and phase field modeling.
    DOI: https://doi.org/10.1515/cmam-2017-0039. Computational Methods in Applied Mathematics (2017) arxiv

  15. H. Antil, J. Pfefferer, and M. Warma.
    A note on semilinear fractional elliptic equation: analysis and discretization.
    DOI: https://doi.org/10.1051/m2an/2017023. Math. Model. Numer. Anal. (ESAIM: M2AN) (2017). arxiv

  16. H. Antil, E. Otarola, and A. J. Salgado.
    Some applications of weighted norm inequalities to the analysis of optimal control problems.
    DOI: https://doi.org/10.1093/imanum/drx018. IMA Journal of Numerical Analysis, 2017. arxiv

  17. H. Antil, and C. N. Rautenberg.
    A Numerical Method for Fractional Elliptic Quasi-Variational Inequalities
    Mathematisches Forschungsinstitut Oberwolfach, Report, 2017. link

  18. H. Antil, and E. Otarola.
    An a posteriori error analysis for an optimal control problem involving the fractional Laplacian.
    DOI: https://doi.org/10.1093/imanum/drx005. IMA Journal of Numerical Analysis (2017). arxiv

  19. H. Antil, M. Heinkenschloss, and S. Hardesty.
    Shape Optimization of Shell Structure Acoustics.
    SIAM J. Control Optim. 55 (3), 1347--1376, 2017.

  20. H. Antil, M. Heinkenschloss, and S. Hardesty.
    Supplementary Materials: Shape Optimization of Shell Structure Acoustics.
    Department of Computational and Applied Mathematics, Rice University (2017). Technical Report

  21. H. Antil, M. Hintermueller, R. H. Nochetto, T. M. Surowiec and D. Wegner.
    Finite Horizon Model Predictive Control of Electrowetting on Dielectric with Pinning.
    Interface and Free Boundaries 19 (1), 1-30, 2017.

  22. K. Carlberg, M. Barone, and H. Antil.
    Galerkin v. discrete-optimal projection in nonlinear model reduction.
    Journal of Computational Physics, 330, 693-734, 2017. arxiv

  23. H. Antil, E. Otarola, and A. J. Salgado.
    A fractional space-time optimal control problem: analysis and discretization.
    SIAM Journal of Control and Optimization, 54(3), 1295-1328, 2016. arxiv

  24. H. Antil, and A. J. Salgado.
    Approximation of elliptic equations with BMO coefficients.
    IMA Journal of Numerical Analysis, 36(1), 222-237, 2016. arxiv

  25. H. Antil, and E. Otarola.
    A FEM for an optimal control problem of fractional powers of elliptic operators.
    SIAM Journal of Control and Optimization, 53(6), 3432-3456, 2015. arxiv

  26. H. Antil, R. H. Nochetto, and P. Sodré.
    Optimal Control of a Free Boundary Problem with Surface Tension Effects: A Priori Error Analysis.
    SIAM J. Numer. Anal. 53, no. 5, 2279-2306, (2015). arxiv

  27. H. Antil, R. H. Nochetto, and P. Sodré.
    Optimal Control of a Free Boundary Problem: Analysis with Second Order Sufficient Conditions.
    SIAM Journal of Control and Optimization (2014), 52(5):2771--2799. arxiv

  28. H. Antil, M. Heinkenschloss, and D. C. Sorensen.
    Application of Discrete Empirical Interpolation Method to Reduced Order Modeling of Nonlinear and Parametric Systems.
    A. Quarteroni and G. Rozzas (eds.), Reduced Order Methods for Modeling and Computational Reduction, Model. Simul.& Appl. Vol. 9, 2014, pp. 101-136, Springer Italia, Milan.
  29. H. Antil, S. Field, F. Herrmann, R. H. Nochetto, and M. Tiglio.
    Two-step Greedy Algorithm for Reduced Order Quadratures.
    Journal of Scientific Computing, 57:604--637, 2013. arxiv
    Reduced Order Quadrature (ROQ) is now part of software package FINESSE used at LIGO. link
    Relevant article: D. Brown, R. Smith, A. Freise (2015) link
  30. H. Antil.
    Optimal Control of a Free Boundary Problem with Surface Tension Effects (2012).
    Mathematisches Forschungsinstitut Oberwolfach, Report No. 57/2012, DOI: 10.4171/OWR/2012/57. link
  31. H. Antil, M. Heinkenschloss, R.H.W. Hoppe, C. Linsenmann, and A. Wixforth.
    Reduced Order Modeling Based Shape Optimization of Surface Acoustic Wave Driven Microfluidic Biochips.
    Mathematics and Computers in Simulation (2012). link
  32. H. Antil, R.H.W. Hoppe, C. Linsenmann, and A. Wixforth.
    Multiscale Aspects in Modeling and Simulation of Surface Acoustic Wave Driven Microfluidic Biochips .
    E-Book Series: Progress in Computational Physics (PiCP) (2011), Volume 2, Bentham Science Publishers. link
  33. H. Antil, M. Heinkenschloss, and R.H.W. Hoppe.
    Domain decomposition and balanced truncation model reduction for shape optimization of the Stokes system.
    Optimization Methods and Software (2011), 26(4-5):643--669. preprint
    Most cited article in this journal. Years 2012-13.
  34. H. Antil, M. Heinkenschloss, R.H.W. Hoppe, and D.C. Sorensen.
    Domain decomposition and model reduction for the numerical solution of PDE constrained optimization problems with localized optimization variables .
    Computing and Visualization in Science (2010), 13(6):249--264. link
  35. H. Antil, R. Glowinski, R.H.W. Hoppe, and C. Linsenmann, T.-W. Pan, and A. Wixforth.
    Modeling, Simulation, and Optimization of Surface Acoustic Wave Driven Microfluidic Biochips .
    Journal of Computational Mathematics (2010), 28(2):149--169. link
  36. H. Antil.
    Shape Optimization Governed by the Heat and the Stokes Equations Using Domain Decomposition and Model Reduction (2009).
    Mathematisches Forschungsinstitut Oberwolfach, Report No. 04/2009, DOI: 10.4171/OWR/2009/04. link
  37. H. Antil, R. H.W. Hoppe, and C. Linsenmann.
    Adaptive Multilevel Interior Point Methods in PDE Constrained Optimization.
    Proc. Int. Conf. on Domain Decomposition Methods and Applications XVIII (M. Bercovier et al.; eds.), Lecture Notes in Computer Science and Engineering (2009), 70:15-26, Springer, Berlin-Heidelberg-New York.
  38. H. Antil, R. H.W. Hoppe, and C. Linsenmann.
    Optimal design of stationary flow problems by path-following interior-point.
    Control and Cybernetics (2008) 37(4):771-796. preprint
  39. H. Antil, R. H.W. Hoppe, and C. Linsenmann.
    Adaptive Path-following Primal-Dual Interior Point Methods for Shape Optimization of Linear and Nonlinear Stokes Flow Problems.
    Lecture Notes in Computer Science (2008), 4818:259-266, Springer, Berlin-Heidelberg-New York.
  40. H. Antil , A. Gantner, R. H.W. Hoppe, D. Koster, K.G. Siebert and A. Wixforth.
    Modeling and Simulation of Piezoelectrically Agitated Acoustic Streaming on Microfluidic Biochips.
    Proc. 17th Int. Conf. on Domain Decomposition Methods (Langer, U. et al.; eds.), Lecture Notes in Computational Science and Engineering (2008), 60:305-312, Springer; Berlin Heidelberg-New York.
  41. H. Antil , R. H.W. Hoppe, and C. Linsenmann.
    Path-following primal-dual interior-point methods for shape optimization of stationary flow problems.
    Journal of Numerical Mathematics (2007) 15(2):81-100. preprint
Others

  1. H. Antil.
    Optimization and Model Reduction of Time Dependent PDE-Constrained Optimization Problems: Applications to Acoustic Wave Driven Microfluidic Biochips.
    PhD Dissertation, Department of Mathematics, University of Houston (2009). online version