INSTITUT FÜR MATHEMATIK UND
WISSENSCHAFTLICHES RECHNEN		 Text Karl-Franzens-Universitaet logo uni graz

Alfio Borzì


Publications


Master Thesis

  1. Sulla Applicazione Rigorosa in Fisica del Calcolo Variazionale,
    Universita' di Catania, 1988. (Supervis. G. Fonte)

  2. Fourier Spectral Methods for Soliton Equations,
    SISSA - Trieste,1990. (Supervis. A. Quarteroni)

Ph.D. Thesis

    New Aspects of Multilevel Methods and Some Applications,
    SISSA - Trieste, 1993. (Supervis. A. Lanza)

Habilitation Thesis

    Multigrid Methods for Optimality Systems, Uni Graz, 2003.

Papers

  1. M. Vallejos and A. Borzì, Multigrid optimization methods for linear and bilinear elliptic optimal control problems,
    to appear in Computing

  2. G. von Winckel and A. Borzì, Computational techniques for a quantum control problem with H1-cost,
    to appear in Inverse Problems

  3. A. Borzì and U. Hohenester, Multigrid optimization schemes for solving Bose--Einstein condensates control problems,
    SIAM J. Sci. Comp., 30 (2008), 441-462

  4. P. Ditz and A. Borzì, A cascadic monotonic time-discretized algorithm for finite-level quantum control computation,
    Computer Physics Communications

  5. A. Borzì, J. Salomon, and S. Volkwein, Formulation and numerical solution of finite-level quantum optimal control problems,
    Journal of Computational and Applied Mathematics, 2007.

  6. 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)

  7. A. Borzì, Smoothers for control- and state-constrained optimal control problems,
    Computing and Visualization in Science, 11 (2008), 59-66.

  8. A. Borzì, On the convergence of the MG/OPT method,
    PAMM, 5(1) (2005), 735-736

  9. 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.

  10. A. Borzì and R. Griesse, Distributed optimal control of lambda-omega systems,
    Journal of Numerical Mathematics, 14 (2006), 17-40.

  11. 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.

  12. 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.

  13. 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.

  14. 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

  15. 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.

  16. 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.

  17. A. Borzì, Solution of lambda-omega systems: Theta-schemes and multigrid methods,
    Numerische Mathematik, 98(4) (2004), 581-606.

  18. A. Borzì and K. Kunisch, A multigrid scheme for elliptic constrained optimal control problems,
    Computational Optimization and Applications, 31 (2005), 309-333.

  19. 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.

  20. 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.

  21. A. Borzì, Multigrid methods for parabolic distributed optimal control problems,
    J. Comp. Appl. Math, 157 (2003), 365-382.

  22. P. Bartsch and A. Borzì, On the Modeling and Simulation of Boundary Flow Through Partially Open Pipe Ends,
    ZAMP, 55 (2004), 946-961.

  23. 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).

  24. A. Borzì, Fast multigrid methods for parabolic optimal control problems,
    Proceedings of 18-th GAMM Seminar Leipzig 2002.

  25. A. Borzì and G. Propst, Numerical Investigation of the Liebau Phenomenon,
    ZAMP, 54 (2003), 1050 - 1072.

  26. G. Propst and A. Borzì, 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.

  27. 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.

  28. A. Borzì, K. Ito, and K. Kunisch, Optimal Control Formulation for Determining Optical Flow,
    SIAM J. Sci. Comput., 24(3) (2002), 818-847.

  29. A. Borzì, K. Ito, and K. Kunisch, An Optimal Control Approach to Optical Flow Computation,
    Int. J. Numer. Meth. Fluids., 40 (2002), 231-240.

  30. 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.

  31. A. Borzi, K.W. Morton, E. Süli and M. Vanmaele, Multilevel Solution of Cell Vertex Cauchy-Riemann Equations,
    SIAM J. Sci. Comp.,18(2) (1997),441-459.

  32. M. Vanmaele, K.W. Morton, E. Süli 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.

  33. A. Borzi and A. Koubek, A multi-grid method for the resolution of thermodynamic Bethe ansatz equations,
    Comp. Phys. Commun., 75, 118-126,(1993).

  34. A. Borzi and G. Fonte, On Variational principles for Nonlinear Partial Differential Equations in Complex Spaces,
    Nuovo Cimento, B107, 189-201,(1992).

  35. 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.

  36. 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.

  37. 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.

  38. 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.

  39. 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.

  40. 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.

  41. A. Borzi, K.W. Morton, E. Süli 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).

  42. A. Borzi, Burgers Equation and Multi-Grid Techniques,
    in "Contributions to Multigrid" ed. bv P.W. Hemker and P. Wesseling, CWI, Amsterdam, (1994).

  43. 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).

  44. 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, Birkhaeuser Verlag, Basel, (1994).

A few old Preprints, Technical Reports, and All That

  1. A. Borzì Introduction to Multilevel Methods,
    Lecture Notes in Mathematics, Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, 1994.

  2. A. Borzi, The Splitting Formulation of Multilevel Methods and Some Applications, technical report NA94/03, Oxford University Computing Laboratory, (1994).

  3. A. Borzi, A cell-faced data structure for the cell-centre discretisation method, technical report CS-0058, AVL LIST GmbH, (1997).

  4. A. Borzì The Development of an Algorithm for the BOOST Modeling of a Perforated Pipe in a Plenum or in a Pipe, Tech. Rep. AST-1999-005, Dr. A. Borzì EDV-Dienstleistung, Graz, 1999.

Published Algorithms

  1. SANTAFE

    A space-time multigrid method for open-loop (and receding-horizon) optimal control of time-dependent reaction-diffusion systems (2005).
    In MGNet: MGNet Home Page    ,

  2. CONTROLLA

    A full multigrid method for the solution of an optimality system arising from a singular optimal control problem.
    In MGNet: MGNet Home Page    ,

  3. INTEGRA

    A multigrid code for the solution of systems of nonlinear integral equations.
    In MGNet: MGNet Home Page    ,

  4. TBA

    A multigrid code for the solution of the thermodynamic Bethe Ansatz equations.
    In CPC Program Library: CPC Program Library Home Page.


    personal, research, teaching

    Research group on Optimal Control and Inverse Problems

    last changed: 30-5-2003