Publications
2024
- A. Borzì, G. Infante, and G. Mascali,
Optimal design of equilibrium solutions of the Vlasov-Poisson system by an external electric field,
SIAM Journal on Applied Mathematics, 2024 (to appear). - N. Vater and A. Borzì,
Convergence of a quasi-Newton method for solving systems of nonlinear underdetermined equations,
Comput Optim Appl (2024).
doi: 10.1007/s10589-024-00606-3 - A. Dey, A. Borzì and S. Roy,
A high contrast and resolution reconstruction algorithm in quantitative photoacoustic tomography,
Journal of Computational and Applied Mathematics, 451 (2024), 116065.
doi: 10.1016/j.cam.2024.116065 - N. Vater and A. Borzì,
A split preconditioning scheme for nonlinear underdetermined least squares problems,
Numerical Linear Algebra with Applications, 2024.
doi: 10.1002/nla.2558 - S. Hofmann and A. Borzì,
Pointwise error estimates of numerical solutions to linear quadratic optimal control problems,
Journal of Scientific Computing, 99 (2024), 21, pp. 1-44.
doi: 10.1007/s10915-024-02484-7 - O. Morandi, N. Rotundo, A. Borzì, L, Barletti,
An optimal control problem for the Wigner equation,
SIAM Journal on Applied Mathematics, 84 (2024), pp. 387-411.
doi: 10.1137/22M1515033 - G. Nastasi, A. Borzì, V. Romano,
Optimal control of a semiclassical Boltzmann equation for charge transport in graphene,
Communications in Nonlinear Science and Numerical Simulation, 2024,
doi: 10.1016/j.cnsns.2024.107933 - J. Bartsch and A. Borzì,
On the stabilization of a kinetic model by feedback-like control fields in a Monte Carlo framework,
Kinetic and Related Models.
doi: 10.3934/krm2024005 - S. Roy and A. Borzì,
Numerical approximation of kinetic Fokker–Planck equations with specular reflection boundary conditions,
Journal of Computational Physics, 503 (2024) 112841.
download: https://authors.elsevier.com/c/1ibF1508H~B25
doi: https://doi.org/10.1016/j.jcp.2024.112841
2023
- M. Annunziato and A. Borzì,
Fokker–Planck Analysis of Superresolution Microscopy Images,
Math. Comput. Appl. 2023, 28(6), 113;
doi: 10.3390/mca28060113 - A. Borzi, K. Kulakowski,
Social balance in oscillatory ecosystems
in Jochen Wittmann, Kurt Chudej (Eds.) Simulation in den Umwelt- und Geowissenschaften,
Workshop Bayreuth 2023, Berichte aus der Umweltinformatik, Shaker Verlag, Düren, 2023. - J. Bartsch, A. Borzì, C. Schenk, D. Schmidt, J. Müller, V. Schulz, K. Velten,
An extended model of wine fermentation including aromas and acids,
in Jochen Wittmann, Kurt Chudej (Eds.) Simulation in den Umwelt- und Geowissenschaften,
Workshop Bayreuth 2023, Berichte aus der Umweltinformatik, Shaker Verlag, Düren, 2023. - J. Kleineisel, K. Lauer, A. Borzì, T. A. Bley, H. Köstler and T. Wech
Assessment of resolution and noise in magnetic resonance images reconstructed by data driven approaches
Zeitschrift für Medizinische Physik,
DOI: 10.1016/j.zemedi.2023.08.007 - Hao Chen and A. Borzì
Positivity Preserving Exponential Integrators for Differential Riccati Equations
Journal of Scientific Computing (2023) 96:50.
DOI: 10.1007/s10915-023-02275-6 - N. Vater and A. Borzì
Preconditioned gradient method for data approximation with shallow neural networks
The 8th International Conference on Machine Learning, Optimization and Data Science
Sept. 18 - 22, 2022, Certosa di Pontignano, Siena – Tuscany, Italy.
LOD 2022 Springer LNCS Conference Proceedings, LNCS 13811, pp. 357-372, 2023.
DOI: 10.1007/978-3-031-25891-6_27 - J. Körner and A. Borzì
Accuracy Estimates for Bilinear Optimal Control Problems Governed by Ordinary Differential Equations
Numerical Functional Analysis and Optimization,
DOI: 10.1080/01630563.2023.2192776
PDF
2022
- J. Körner and A. Borzì
Second–order analysis of Fokker–Planck ensemble optimal control problems
ESAIM: COCV, Forthcoming article,
DOI: 10.1051/cocv/2022066
PDF (462.8 KB)
Instability of oscillations in the Rosenzweig–MacArthur model of one consumer and two resources
Chaos: An Interdisciplinary Journal of Nonlinear Science, (Vol.32, Issue 9)
DOI: 10.1063/5.0105340- N. Vater and A. Borzì
Training artificial neural networks with gradient and coarse-level correction schemes
Machine Learning, Optimization, and Data Science
7th International Conference, Grasmere, UK, October 4–8, 2021.
LOD 2021 Springer LNCS Conference Proceedings, LNCS 13163, pp. 473-487, 2022
DOI: 10.1007/978-3-030-95467-3_34 - H. Weinmann, K. Kułakowski and A. Borzì
Ecosystem models and social balance from a synchronization perspective
International Journal of Modern Physics C, 2021,
DOI: 10.1142/S0129183122500644 - S. Hofmann, A. Borzì
A sequential quadratic hamiltonian algorithm for training explicit RK neural networks
Journal of Computational and Applied Mathematics, Vol. 405, 2022,
DOI: 10.1016/j.cam.2021.113943
2021
- D. Gathungu, M. Bebendorf and A. Borzì,
Hierarchical-matrix method for a class of diffusion-dominated partial integro-differential equations,
Numerical Linear Algebra with Applications (2021). - F. Calà Campana, A. De Marchi, A. Borzì and M. Gerdts,
On the numerical solution of a free end-time homicidal chauffeur game,
FGS’2019, ESAIM: Proceedings and Surveys, 71 (2021), 33-42. - J. Bartsch, A. Borzì, F. Fanelli, S. Roy
- A numerical investigation of Brockett’s ensemble optimal control problems,
Numerische Mathematik (2021).
Free e-print - M. Annunziato and A. Borzì,
A sequential quadratic Hamiltonian scheme to compute optimal relaxed controls,
ESAIM: Control, Optimisation and Calculus of Variations, ESAIM: COCV Volume 27, (2021) 49. - J. Bartsch, A. Borzì,
MOCOKI: A Monte Carlo approach for optimal control in the force of a linear kinetic model
Computer Physics Communications, Volume 266, September (2021), 108030. - M. Annunziato and A. Borzì,
A Fokker--Planck Approach to the Reconstruction of a Cell Membrane Potential,
SIAM Journal on Scientific Computing, 43(3), B623–B649 (2021). - F. Calà Campana, A. Borzì,
On the SQH Method for Solving Differential Nash Games,
Journal of Dynamical and Control Systems (2021).
Free e-print - J. Bartsch, G. Nastasi, A. Borzì,
Optimal Control of the Keilson-Storer Master Equation in a Monte Carlo Framework,
Journal of Computational and Theoretical Transport (2021), Pages 454-482.
Free e-print
2020
- A.Borzì,
The Fokker-Planck framework in the modeling of pedestrians’ motion,
Chapter 6 in: L. Gibelli (ed.), Crowd Dynamics, Volume 2,
Modeling and Simulation in Science, Engineering and Technology, Birkhäuser, Cham, Switzerland (2020), 111-131 - A. Borzì and L. Grüne,
Towards a solution of mean-field control problems using model predictive control ,
IFAC-PapersOnLine, 53, 4973-4978 (2020) . - T. Breitenbach, A. Borzì,
The Pontryagin maximum principle for solving Fokker-Planck optimal control problems,
Computational Optimization and Applied Mathematics, 76, 499–533 (2020). - F. Calà Campana, G. Ciaramella, A. Borzì,
Nash equilibria and bargaining solutions of differential bilinear games ,
Dynamic Games and Applications 11, pages 1–28 (2020).
Free e-print
2019
- T. Breitenbach, A. Borzì,
A sequential quadratic Hamiltonian scheme for solving non-smooth quantum control problems with sparsity,
Journal of Computational and Applied Mathematics Vol. 369 (2019) 112583. - Jan Bartsch, A. Borzì, Francesco Fanelli, Souvik Roy,
A theoretical investigation of Brockett’s ensemble optimal control problems
Calculus of Variations and Partial Differential Equations 58, Article number: 162 (2019).
Free e-print - T. Breitenbach, A. Borzì,
On the SQH scheme to solve non-smooth PDE optimal control problems,
Numerical Functional Analysis and Optimization, Vol. 40, 1489-1531 (2019).
Free e-print
2018
- T. Breitenbach, A. Borzì,
A Sequential Quadratic Hamiltonian Method for Solving Parabolic Optimal Control Problems with Discontinuous Cost Functionals,
Journal of Dynamical and Control Systems, 25, pages 403–435 2018.
Preprint - M.-L. Kienle Garrido, T. Breitenbach, K. Chudej, A. Borzì,
Modeling and Numerical Solution of a Cancer Therapy Optimal Control Problem,
Applied Mathematics, Vol.9 No.8 (2018). - S. Roy, A. Borzì,
A new optimisation approach to sparse reconstruction of log-conductivity in acousto-electric tomography,
SIAM Journal on Imaging Sciences, 11 (2018), 1759-1784. - M. Annunziato and A. Borzì,
A Fokker-Planck Control Framework for Stochastic Systems,
EMS Surveys In Mathematical Sciences, 5 (2018), 65-98.
Preprint
2017
- K. Kułakowski, P. Gronek and A. Borzì,
Paradox of integration - mean field approach,
International Journal of Modern Physics C (IJMPC), 28 (2017), 1750133 - M. Sprengel, G. Ciaramella and A. Borzì,
Investigation of optimal control problems governed by a time-dependent Kohn-Sham model,
Journal of Dynamical and Control Systems, 24 (2018), 657-679 - D.K. Gathungu and A. Borzì,
A multigrid scheme for solving convection-diffusion-integral optimal control problems,
Computing and Visualization in Science, 2017 - B. Gaviraghi, Mario Annunziato, Alfio Borzì,
Chapter 22: Splitting Methods for Fokker-Planck Equations Related to Jump-Diffusion Processes, pp. 409-422
Chapter 23: A Fokker-Planck Based Approach to Control Jump Processes, pp. 423-439
Novel Methods in Computational Finance, Springer, 2017 - Edited by Matthias Ehrhardt, Michael Guenther, E. Jan W. ter Maten.
S. Roy, A. Borzì, A. Habbal,
Pedestrian motion modelled by Fokker - Planck Nash games,
Royal Society open science, 4: 170648, 2017. (open access) - S. Roy, A. Annunziato, A. Borzì, C. Klingenberg,
A Fokker-Planck approach to control collective motion,
Computational Optimization and Applications, 2017. - D.K. Gathungu and A. Borzì,
Multigrid Solution of an Elliptic Fredholm Partial Integro-Differential Equation with a Hilbert-Schmidt Integral Operator,
Applied Mathematics, 8 (2017), 967-986. - T. Breitenbach, M. Annunziato and A. Borzì,
On the optimal control of a random walk with jumps and barriers,
Methodology and Computing in Applied Probability, 2017 - G. Ciaramella, M. Sprengel & A. Borzi,
A theoretical investigation of time-dependent Kohn–Sham equations: new proofs,
Applicable Analysis, 2019. - M. Sprengel, G. Ciaramella and A. Borzì,
A theoretical investigation of time-dependent Kohn-Sham equations,
SIAM Journal on Mathematical Analysis, 49 (2017), 1681-1704.
Errata - S. Roy and A. Borzì,
Numerical Investigation of a Class of Liouville Control Problems,
Journal of Scientific Computing, 73 (2017), 178-202. - M. Sprengel, G. Ciaramella and A. Borzì,
A COKOSNUT code for the control of the time-dependent Kohn-Sham model,
Computer Physics Communications, 214 (2017), 231-238.
Free download until April 19, 2017 - Juri Merger and Alfio Borzì,
Dynamics identification in evolution models using radial basis functions,
Journal of Dynamical and Control Systems, 23 (2017), 317-335. - J. Merger, A. Borzì, and R. Herzog,
Optimal Control of a System of Reaction-Diffusion Equations Modeling the Wine Fermentation Process,
Optimal Control, Applications and Methods, 38 (2017), 112-132. - Andrea Thomann and Alfio Borzì,
Stability and accuracy of a pseudospectral scheme for the Wigner function equation,
Numerical Methods for Partial Differential Equations, 33 (2017), 62-87. - Andreas Schindele and Alfio Borzì,
Proximal schemes for parabolic optimal control problems with sparsity promoting cost functionals,
International Journal of Control, 90 (2016), 2349-2367.
2016
- Beatrice Gaviraghi, Mario Annunziato, Alfio Borzì, Analysis of splitting methods for solving a partial-integro differential Fokker-Planck equation,
Applied Mathematics and Computation, 294 (2016), 1-17. - Beatrice Gaviraghi, Andreas Schindele, Mario Annunziato, Alfio Borzì, On optimal sparse-control problems governed by jump-diffusion processes,
Applied Mathematics 7 (2016), 1978-2004. - Andreas Schindele and Alfio Borzì, Proximal Methods for Elliptic Optimal Control Problems with Sparsity Cost Functional,
Applied Mathematics, 7 (2016), 967-992. - Juri Merger and Alfio Borzì, A Lie Algebraic and Numerical Investigation of the Black-Scholes Equation with Heston Volatility Model,
J Generalized Lie Theory Appl (2016). - Alfio Borzì and Marco Caponigro,
A control theoretical approach to crowd management:
Physics of Life Reviews, 18 (2016), 27-28.
Comment on 'Human behaviours in evacuation crowd dynamics: From modelling to big data toward crisis management' by Nicola Bellomo et al., - V. Ratz, T. Wech, A. Schindele, A. Dierks, A. Sauer, J. Reibetanz, A. Borzì, T. Bley, H. Koestler, Dynamic 3D MR-Defecography,
Fortschr. Roentgenstr, 188(09)(2016), 859-863. - Souvik Roy, Mario Annunziato, and Alfio Borzì, A Fokker--Planck feedback control-constrained approach for modelling crowd motion,
Journal of Computational and Theoretical Transport, 45 (2016), 442-458. - Gabriele Ciaramella and Alfio Borzì, Quantum Optimal Control Problems with a Sparsity Cost Functional,
Numerical Functional Analysis and Optimization, 37 (2016), 938-965. - V. Thalhofer, M. Annunziato, and A. Borzì, Stochastic modelling and control of antibiotic subtilin production,
Journal of Mathematical Biology, 73 (2016), 727-749. - M. Mohammadi and A. Borzì, Hermite approximation of a hyperbolic Fokker-Planck optimality system to control a piecewise-deterministic process,
International Journal of Control, 89 (2016), 1382-1395. - G. Ciaramella and A. Borzì, A LONE code for the sparse control of quantum systems,
Computer Physics Communications, 200 (2016), 312-323. - T. Wech, N. Seiberlich, A. Schindele, V. Grau, L. Diffley, M. L. Gyngell, A. Borzì, H. Koestler, and J. E. Schneider ,
Development of Real-time Magnetic Resonance Imaging of Mouse Hearts at 9.4 Tesla -- Simulations and First Application,
IEEE TRANSACTIONS ON MEDICAL IMAGING, 35(3):912-20. - A. Borzì, E.-J. Park, M. Vallejos Lass, Multigrid Optimization Methods for the Optimal Control of Convection -- Diffusion Problems with Bilinear Control,
Journal of Optimization Theory and Applications, 168 (2016), 510-533. - M. Annunziato, A. Borzì, M. Magdziarz, A. Weron, A fractional Fokker-Planck control framework for subdiffusion processes,
Optimal Control, Applications and Methods, 37 (2016), 290-304
2015
- S. Wongkaew, M. Caponigro, K. Kułakowski, A. Borzì, On the control of the Heider balance model,
European Physical Journal - Special Topics, 224(2015), 3325-3342. - G. Ciaramella and A. Borzì, SKRYN: A fast semismooth-Krylov-Newton method for controlling Ising spin systems,
- Computer Physics Communications, 190 (2015), 213-223.
- G. Ciaramella, A. Borzì, G. Dirr, D. Wachsmuth, Newton methods for the optimal control of closed quantum spin systems,
SIAM Journal on Scientific Computing, 37 (2015), A319-A346. - G. Ciaramellaa , J. Salomon, A. Borzì, A method for solving exact-controllability problems governed by closed quantum spin systems,
International Journal of Control (IJC), 88 (2015), 682-702. - Masoumeh Mohammadi and Alfio Borzì, A Hermite spectral method for a Fokker-Planck optimal control problem in an unbounded domain,
International Journal for Uncertainty Quantification (IJUQ), 5 (2015), 233-254. - Mohammad Tanvir Rahman and Alfio Borzì, A FEM-multigrid scheme for elliptic Nash-equilibrium multiobjective optimal control problems,
Numerical Mathematics: Theory, Methods and Applications (NMTMA), 8 (2015) 253-282. - Suttida Wongkaew, Marco Caponigro, Alfio Borzì, On the control through leadership of the Hegselmann-Krause opinion formation model,
Mathematical Models and Methods in Applied Sciences (M3AS), 25 (2015), 565-585. - S. Wongkaew and A. Borzì, Modeling and control through leadership of a refined flocking system,
Mathematical Models and Methods in Applied Sciences (M3AS), 25 (2015), 255-282. - S. Gonzalez Andrade and A. Borzì, Second-order approximation and fast multigrid solution of parabolic bilinear optimization problems,
Advances in Computational Mathematics, 41 (2015), 457-488 - M. Mohammadi and A. Borzì, Analysis of the Chang-Cooper Discretization Scheme for a Class of Fokker-Planck Equations,
Journal of Numerical Mathematics, 23 (2015), 271-288.
2014
- M. Annunziato, A. Borzì, F. Nobile, and R. Tempone, On the connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck control frameworks,
Applied Mathematics, 5 (2014), 2476-2484. - M. Annunziato and A. Borzì, Optimal control of a class of piecewise deterministic processes ,
European Journal of Applied Mathematics, 25 (2014), 1-25.
2013
- A. Borzì, Daniela di Serafino, and Valentina De Simone, Parallel algebraic multilevel Schwarz preconditioners for a class of elliptic PDE systems,
Computing and Visualization in Science, 16 (2013), 1-14. - P.F. Antonietti, A. Borzì, and M. Verani, Multigrid shape optimization governed by elliptic PDEs,
SIAM J. Control Optim., 51 (2013), 1417-1440. - A. Borzì, Quantum optimal control using the adjoint method,
Nanoscale Systems: Mathematical Modeling, Theory and Applications, 1 (2012), 93-111. - Davide Calebiro, Finn Rieken, Julia Wagner, Titiwat Sungkaworn, Ulrike Zabel, Alfio Borzì, Emanuele Cocucci, Alexander Zuern, Martin J. Lohse,
Single-molecule analysis of fluorescently labeled GPCRs reveals receptor-specific complexes with distinct dynamics and organization,
Proceedings of the National Academy of Sciences (PNAS), 110 (2013), 743-748. - M. Annunziato and A. Borzì, Fokker-Planck-based control of a two-level open quantum system,
Mathematical Models and Methods in Applied Sciences (M3AS), 23 (2013), 2039-2064 - A. Borzì and C. Kanzow, Formulation and numerical solution of Nash equilibrium multiobjective elliptic control problems,
SIAM J. Control Optim., 51(2013), 718-744. - M. Annunziato and A. Borzì, A Fokker-Planck control framework for multidimensional stochastic processes,
Journal of Computational and Applied Mathematics, 237 (2013), 487-507.
2012
- S. Gonzalez Andrade and A. Borzi, Multigrid solution of a Lavrentiev-regularized state-constrained parabolic control problem,
Numerical Mathematics: Theory, Methods and Applications, 5 (2012), 1-18. - S. Gonzalez Andrade and A. Borzì, Multigrid second-order accurate solution of parabolic control-constrained problems,
Computational Optimization and Applications, 51 (2012), 835-866. - A. Borzì and M. Borzì, A MPC Scheme with Guaranteed Stability for the Control of Bloch Systems,
Proceedings MATHMOD 2012, I. Troch, F. Breitenecker, eds.
2011
- M. M. Butt and A. Borzì, A full multigrid solution of control-constrained Cauchy-Riemann optimal control problems ,
Journal of Numerical Mathematics, 19 (2011), 189-214. - A. Borzì and G. von Winckel, A POD framework to determine robust controls in PDE optimization,
Computing and Visualization in Science, 14 (2011), 91-103. - M. M. Butt and A. Borzì, Formulation and multigrid solution of Cauchy-Riemann optimal control problems,
Computing and Visualization in Science, 14 (2011), 79-90.
2010
- M. Annunziato and A. Borzì, Optimal control of probability density functions of stochastic processes,
Mathematical Modelling and Analysis, 15 (2010), 393-407. - G. von Winckel and A. Borzì, QUCON: A fast Krylov-Newton code for dipole quantum control problems,
Computer Physics Communications, 181 (2010), 2158-2163. - A. Borzì, V. Schulz, C. Schillings, and G. von Winckel, On the treatment of distributed uncertainties in PDE constrained optimization,
GAMM Mitteilungen, 33 (2010), 230-246. - A. Borzì, Multigrid and sparse-grid schemes for elliptic control problems with random coefficients,
Computing and Visualization in Science, 13 (2010), 153-160. - M. Annunziato and A. Borzì, Fast solvers of Fredholm optimal control problems,
Numerical Mathematics: Theory, Methods and Applications, 3 (2010), 431-448.
2009
- A. Borzì, M. di Bisceglie, C. Galdi, G. Giangregorio, Robust registration of satellite images with local distorsions,
Proceedings IEEE International Geoscience & Remote Sensing Symposium July 12-17, 2009, Cape Town, South Africa - G. von Winckel, A. Borzì, and S. Volkwein, A globalized Newton method for the accurate solution of a dipole quantum control problem,
SIAM J. Sci. Comp., 31 (2009), 4176-4203 - A. Borzì and G. von Winckel, Multigrid methods and sparse-grid collocation techniques for parabolic optimal control problems with random coefficients,
SIAM J. Sci. Comp., 31 (2009), 2172-2192 - A. Borzì and V. Schulz, Multigrid methods for PDE optimization,
SIAM Review, 51 (2009), 361-395. - O. Lass, M. Vallejos, A. Borzì, and C.C. Douglas, Implementation and analysis of multigrid schemes with finite elements for elliptic optimal control problems,
Computing, 84 (2009), 27-48
2008
- M. Vallejos and A. Borzì, Multigrid optimization methods for linear and bilinear elliptic optimal control problems,
- Computing, 82 (2008), 31-52
- M. Vallejos and A. Borzì, Multigrid methods for linear elliptic optimal control problems,
Numerical Mathematics and Advanced Applications, Springer (2008) - G. von Winckel and A. Borzì, Computational techniques for a quantum control problem with H1-cost,
Inverse Problems, 24 (2008) 034007. - A. Borzì and U. Hohenester, Multigrid optimization schemes for solving Bose--Einstein condensates control problems,
SIAM J. Sci. Comp., 30 (2008), 441-462 - P. Ditz and A. Borzì, A cascadic monotonic time-discretized algorithm for finite-level quantum control computation,
Computer Physics Communications, 178 (2008), 393-399. - A. Borzì, J. Salomon, and S. Volkwein, Formulation and numerical solution of finite-level quantum optimal control problems,
Journal of Computational and Applied Mathematics,216 (2008), 170-197 - A. Borzì, Smoothers for control- and state-constrained optimal control problems,
Computing and Visualization in Science, 11 (2008), 59-66.
2007
- U. Hohenester, P.K. Rekdal, A. Borzì, J. Schmiedmayer, Optimal quantum control of Bose-Einstein condensates in magnetic microtraps,
Phys. Rev. A 75, 023602 (2007) - A. Borzì, High-order discretization and multigrid solution of elliptic nonlinear constrained optimal control problems,
Journal of Computational and Applied Mathematics, 200 (2007), 67-85. - A. Borzì, Space-time multigrid methods for solving unsteady optimal control problems, (Chapter 5) in L.T. Biegler, O. Ghattas, M. Heinkenschloss, D. Keyes and B. van Bloemen Waanders (Eds.),
Real-Time PDE-Constrained Optimization, Computational Science and Engineering, Vol. 3, SIAM, Philadelphia, 2007.
2006
- A. Borzì and R. Griesse, Distributed optimal control of lambda-omega systems,
Journal of Numerical Mathematics, 14 (2006), 17-40. - A. Borzì and G. Borzì, Algebraic multigrid methods for solving generalized eigenvalue problems,
International Journal for Numerical Methods in Engineering, 65(8) (2006), 1186-1196. - A. Borzì and E. Decker, Analysis of a leap-frog pseudospectral scheme for the Schroedinger equation,
Journal of Computational and Applied Mathematics, 193(1) (2006), 65-88. - A. Borzì and K. Kunisch, A globalization strategy for the multigrid solution of elliptic optimal control problems,
Optimization Methods and Software, 21(3) (2006), 445-459
2005
- A. Borzì, On the convergence of the MG/OPT method,
PAMM, 5(1) (2005), 735-736 - A. Borzì, H. Grossauer, and O. Scherzer, Analysis of Iterative Methods for Solving a Ginzburg-Landau Equation,
Int. Journal of Computer Vision, 64 (2005), 203-219. - A. Borzì and R. Griesse, Experiences with a space-time multigrid method for the optimal control of a chemical turbulence model,
Int. J. Numer. Meth. Fluids., 47 (2005), 879-885. - A. Borzì and K. Kunisch, A multigrid scheme for elliptic constrained optimal control problems,
Computational Optimization and Applications, 31 (2005), 309-333.
2004
- A. Borzì, Solution of lambda-omega systems: Theta-schemes and multigrid methods,
Numerische Mathematik, 98(4) (2004), 581-606. - A. Borzì and G. Borzì, An efficient algebraic multigrid method for solving optimality systems,
Computing and Visualization in Science, 7(3/4) (2004), 183-188. - P. Bartsch and A. Borzì, On the Modeling and Simulation of Boundary Flow Through Partially Open Pipe Ends,
ZAMP, 55 (2004), 946-961.
2003
- A. Borzì and G. Borzì, An algebraic multigrid method for a class of elliptic differential systems,
SIAM J. Sci. Comp., 25(1) (2003), 302-323. - A. Borzì, Multigrid methods for parabolic distributed optimal control problems,
J. Comp. Appl. Math, 157 (2003), 365-382. - A. Borzì and G. Propst, Numerical Investigation of the Liebau Phenomenon,
ZAMP, 54 (2003), 1050 - 1072. - A. Borzì, K. Kunisch, and Do Y. Kwak, Accuracy and Convergence Properties of the Finite Difference Multigrid Solution of an Optimal Control Optimality System,
- SIAM J. Control Opt., 41(5) (2003), 1477-1497.
2002
- A. Borzì, G. Stadler, and U. Hohenester, Optimal quantum control in nanostructures: Theory and application to a generic three-level system ,
Phys. Rev. A 66, 053811 (2002). - A. Borzì, Fast multigrid methods for parabolic optimal control problems,
Proceedings of 18-th GAMM Seminar Leipzig 2002. - G. Propst and A. Borzi,
Numerical Investigation of periodically excited valveless pumping,
in Simplicity behind Complexity, W. Klonowski (Ed.), Proceedings of Euroattractor 2002, Warsaw, Pabst science publishers, pp. 192-200 - A. Borzì, K. Ito, and K. Kunisch, Optimal Control Formulation for Determining Optical Flow,
SIAM J. Sci. Comput., 24(3) (2002), 818-847. - A. Borzì, K. Ito, and K. Kunisch, An Optimal Control Approach to Optical Flow Computation,
Int. J. Numer. Meth. Fluids., 40 (2002), 231-240.
until 2000
- A. Borzì and K. Kunisch, The Numerical Solution of the Steady State Solid Fuel Ignition Model and Its Optimal Control,
SIAM J. Sci. Comp., 22(1) (2000), 263-284. - A. Borzi, K.W. Morton, E. Suli and M. Vanmaele, Multilevel Solution of Cell Vertex Cauchy-Riemann Equations,
SIAM J. Sci. Comp.,18(2) (1997),441-459. - M. Vanmaele, K.W. Morton, E. Suli and A. Borzi, Analysis of the Cell Vertex Finite Volume Method for the Cauchy-Riemann Equations,
SIAM J. Num. Anal., 34(5) (1997), 2043-2062. - A. Borzi and A. Koubek, A multi-grid method for the resolution of thermodynamic Bethe ansatz equations,
Comp. Phys. Commun., 75 (1993), 118-126. - A. Borzi and G. Fonte, On Variational principles for Nonlinear Partial Differential Equations in Complex Spaces,
Nuovo Cimento, B107 (1992), 189-201. - A. Borzì, K. Ito and K. Kunisch An Optimal Control Approach to Optical Flow Computation,
In M J Baines, editor, Numerical Methods for Fluid Dynamics VII, ICFD, Oxford University Computing Laboratory, 2001. - P. Bartsch, B. Bachner, A. Borzì, and H.A. Schuemie,
Simulation of a Concentric-Tube Resonator,
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