Publications
2023
- 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,
in International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows 5th ISAIF, 4 - 7 September 2001 Gdansk. - A. Borzì and K. Kunisch, A Multigrid Method for the Optimal Control of Time-Dependent Reaction Diffusion Processes,
in K.H. Hoffmann, R. Hoppe, and V. Schulz (Eds.), „Fast solution of discretized optimization problems“, International Series on Numerical Mathematics, Vol. 138, Birkhäuser, 2001. - A. Borzì and G. Borzì, Algebraic Multigrid and Conjugate Gradient Methods for the Solution of FEM Equations for 3D Static Problems,
9th IGTE Symposium on Numerical Field Calculation in Electrical Engineering, Graz (Austria), 11-14 settembre, 2000. - P. Bartsch and A. Borzì, A New Reconstruction Technique for the Euler Equations of Gas Dynamics with Source Terms,
in E. Toro (Ed.), „Godunov Methods: Theory and Applications“, Kluwer Academic/Plenum Publishers, 2001. - A. Borzì, K. Kunisch, and M. Vanmaele, A Multi-Grid Approach to the Optimal Control of Solid Fuel Ignition Problems,
in E. Dick, K. Riemslagh and J. Vierendeels (Eds.), Lecture Notes in Computer Science and Engineering, 14, European Multigrid Meeting 1999, Springer 2000. - A. Borzi, K.W. Morton, E. Suli and M. Vanmaele, A full multi-grid method for the solution of the cell vertex Cauchy-Riemann equations,
in "Seventh Copper Mountain Conference on Multigrid Methods", ed. by N.D. Melson, T.A. Manteuffel, S.F. McCormick and C.C. Douglas, 73-86, NASA, Hampton, (1996). - A. Borzi, Burgers Equation and Multi-Grid Techniques,
in "Contributions to Multigrid" ed. bv P.W. Hemker and P. Wesseling, CWI, Amsterdam, (1994). - A. Borzi, On the Extension of the Twolevel Method for Operator Equations in Hilbert Space,
in "Contributions to Multigrid" ed. bv P.W. Hemker and P. Wesseling, CWI, Amsterdam, (1994). - A. Borzi and A. Koubek, On a multi-grid algorithm for the TBA equations,
in "Multigrid Methods IV", ed. by P.W. Hemker and P. Wesseling, Birkhäuser Verlag, Basel, (1994).
