PUBLICATIONS

P.Pietra: An up-wind finite element method for a filtration problem. R.A.I.R.O. Num.An. 16 (1982), 463-481.
L.D.Marini, P.Pietra: Fixed-point algorithms for stationary flow in porous media. Comput.Meths.Appl.Mech.Engrg. 56 (1986), 17-45.
L.D.Marini, P.Pietra: Solution of filtration problems through porous media: The programs PIGRA, DAMIAN, PLOTDAM. Pubbl. 395 IAN-CNR, Pavia,(1984), 1-26
P.Pietra, C.Verdi: Convergence on the approximate free boundary for the multi dimensional one-phase Stefan problem. Comp.Mech.Int.J. 1 (1986), 115-125.
P.Pietra, C.Verdi: On the convergence of the approximate free boundary for the parabolic obstacle problem. Rend.Acc.Naz.Lincei, Serie VIII , LXXIX (1985), 159-171.
J.Douglas Jr., P.Pietra: A description of some alternating-direction iterative techniques for mixed finite element methods. Proc. SIAM Meeting , Houston 1985 pp.37-53.
J.Douglas Jr., R.Duran, P.Pietra: Formulation of alternating direction iterative methods for mixed methods in three space. Pubbl. 484 IAN-CNR, Pavia,pp.1-10 (1985) (Proc. ISNA, Madrid, 1985).
J.Douglas Jr., R.Duran , P.Pietra: Alternating-direction iteration for mixed finite element methods. Pubbl. 485 IAN-CNR, Pavia, pp.1-16 (1985) (Proc. 7th Intern. Conf. on Comput. Methods in Appl. Sci. and Engrg.-I.N.R.I.A., 1985).
L.D.Marini, P.Pietra: Alternating Direction Iterative Methods for a Class of Mixed Finite Elements. Pubbl. 510 IAN-CNR, Pavia (1986), 1-18.
F.Brezzi, L.D.Marini, P.Pietra: Méthodes d'éléments finis mixtes et schéma de Scharfetter-Gummel. C.R.Acad.Sci. Paris , 305, Série I, (1987), 599-604.
F.Brezzi, L.D.Marini, P.Pietra: Méthodes d'éléments finis mixtes et schéma de Scharfetter-Gummel. Pubbl. 567 IAN-CNR, Pavia (1987), 1-10.
F.Brezzi, L.D.Marini, P.Pietra: Two-dimensional exponential fitting and applications to semiconductor device equations. SIAM J.Numer.Anal.,26 (1989), 1342-1355.
F.Brezzi, L.D.Marini, P.Pietra: Numerical simulation of semiconductor devices. Comp.Meths. Appl.Mech.Engrg.,75 (1989) 493-514.
C.Canuto, P.Pietra: Boundary and interface Conditions in Finite Element Preconditioners for Chebyshev Methods. J. of Comp. Phys.91 (1990), 310-343.
L.D.Marini, P.Pietra: An Abstract Theory for Mixed Approximations of Second Order Elliptic Problems. Mat. Aplic. Comput.8 (1989), 219-239. (paper)
F.Brezzi, L.D.Marini, P.A.Markowich, P.Pietra: On some numerical problems in semiconductor device simulation. in Mathematical Aspects of Fluid and Plasma Dynamics, (G.Toscani, V.Boffi, S.Rionero Eds.), Lectures Notes in Mathematics 1460, Springer Verlag (1991) 31-42. (paper)
L.D.Marini, P.Pietra: New Mixed Finite Element Schemes for Current Continuity Equations. COMPEL ,9 (1990), 257-268. (paper)
F.Brezzi, L.D.Marini, P.Pietra: Mixed exponential fitting schemes for current continuity equations. In Proc. 6-th Int. NASECODE Conference, Dublin, 11-14 July 1989.
F.Brezzi, L.D.Marini, P.Pietra: On some recent results on the numerical problems in semiconductor device simulation. Proc. EQUADIFF VII Conference, Praga, Agosto 1989.
F.Brezzi, L.D.Marini, P.Pietra: Metodi misti di exponential fitting per le equazioni di continuità della corrente. Rend. Sem. Mat. Fis. Milano, LIX (1989), 137-147.
F.Brezzi, L.D.Marini, P.Pietra: Mixed and hybrid exponential fitting schemes for the drift-diffusion equations in semiconductors. Proc. of the 8th France-Italy-U.R.S.S. Joint Symposium, Pavia,Ottobre1989, I.A.N.,C.N.R. (1989), 39-60 .
L.D.Marini, P.Pietra: A monotonic mixed finite element on rectangles for second order elliptic problems. Mat. Aplic. Comp.,10, Spec. Issue on Innovative Finite Element Methods (1991), 236-277.
U.Ascher, P.A.Markowich, P.Pietra, C.Schmeiser: A phase plane analysis of transonic solutions for the hydrodynamic semiconductor model, Math.Mod. and Meth.in the Appl.Sci., 1 (1991), 347-376.
P.A.Markowich, P.Pietra: A Non-isentropic Euler-Poisson Model for a Collisionless Plasma. Math.Meth. in the Appl.Sci., 16 (1993), 409-442.
L.D.Marini, P.Pietra: Finite element approximation of a degenerate eigenvalue problem. in Boundary Value Problems for Partial Differential Equations and Applications, (J.L.Lions and C.Baiocchi, Eds.), Masson (1993), 393-398.
L.D.Marini, P.Pietra: Mixed finite element approximation of a degenerate elliptic problem. Numer. Math., 71 (1995) 225-236. (paper)
F.Brezzi, L.D.Marini, P.Pietra, A.Russo: A monotonic scheme for advection diffusion problems. Trans. Theory and Stat. Phys.25 (1996) 463-475.
S.Bertoluzza, P.Pietra: Adaptive Wavelet Collocation for Nonlinear BVP's. 12th Int. Conf. on Analysis and Optimization of Systems, Images, Wavelets and PDE's , Paris, June 1996.
A.Jüngel-P.Pietra: A discretization scheme for a quasi, hydrodynamic semiconductor model. Math.Mod. and Meth.in the Appl.Sci 7 (1997), 935-955. (paper)
P.A.Markowich, P.Pietra, C.Pohl: Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit. Numer. Math. 81 (1999), 595-630.
P.Pietra, C.Pohl: Weak limits of the Quantum Hydrodynamic Model, Proc. International Workshop on Quantum Kinetic Theory, Breckenridge, Colorado (USA), August 1997, Special Issue of VLSI Design 9 (1999), 427-434. (paper)
P.A.Markowich, P.Pietra, C.Pohl: Semiclassical analysis of discretizations of Schrödinger, type equations. Proc. International Workshop on Quantum Kinetic Theory, Breckenridge, Colorado (USA), August 1997, Special Issue of VLSI Design 9 (1999), 397-413.
P.A.Markowich, P.Pietra, C.Pohl : A Wigner Measure Approach to the Analysis of Difference Methods for Schrödinger-type Equations. Proc. ENUMATH 97 , Heidelberg (Germany), September 1997.
F.Brezzi, M.Manzini, L.D.Marini, P.Pietra, A.Russo: Discontinous Finite Elements for Diffusion Problems Francesco Brioschi (1824-1897), Convegno di Studi Matematici, Ottobre 22-23 1997, Ist.Lomb. Acc.Sc.Lett., Incontro di Studio N.16 (1999), 197-217. (paper)
S.Bertoluzza, P.Pietra: Space- Frequency Adaptive Approximation for Quantum Hydrodynamic Models, Proc. Mathematical Aspects in Fluid and Plasma Dynamics, Maui, Hawaii (USA), 28 June - 3 Juli 1998. Special Issue of Trans. Theory and Stat. Phys. 29 (2000), 375-395. (paper)
P.Degond, A.Jüngel, P.Pietra: Numerical discretization of energy-transport models for semiconductors with non-parabolic band structure, SIAM Jour. Scien.Comp. 22 (2000), 986-1007. (paper)
F.Brezzi, M.Manzini, L.D.Marini, P.Pietra, A.Russo: Discontinous Galerkin approximations for elliptic problems, Numerical Methods for Pde's, Numer. Methods Partial Differential Eq. 16, (2000), 365-378. (paper)
R.Kosik, P.Fleischman, B.Haindl, P.Pietra, S.Selberherr On the Interplay between Meshing and Discetization in Three-Dimensional Diffusion Simulation, IEEE Trans. CAD Integrated Circuits and Systems 19 (2000), 1233-1240.
P.A.Markowich, P.Pietra, C.Pohl, P.H.Stimming A Wigner-Measure Analysis of the Dufort-Frankel Scheme for the Schrödinger Equation, SIAM Numer.Anal. , 40 (2002), 1281-1310.
M.Burger, H.W.Engl, P.A.Markowich, P.Pietra: Identification of Doping Profiles in Semiconductor Devices, Inverse Problems 17 (2001), 1765-1795. (paper)
S.Holst, A.Jüngel, P.Pietra: A mixed finite element discretization of the energy-transport models for semiconductors, to appear in SIAM Jour. Scien.Comp. (paper)

G.Gazzaniga, P.Lanucara, P.Pietra, S.Rovida and G.Sacchi: Rapid parallelization of the drift diffusion model for semiconductor devices, to appear in Proceedings of EWOMP 2002 , September 18-20, 2002, Rome (paper)

F.Brezzi, L.D.Marini, S. Micheletti, P.Pietra, R. Sacco, and S. Wang: Finite element and finite volume discretizations of Drift-Diffusion type fluid models for semiconductors , to appear in Numerical Methods for Electrodynamic Problems , W.H.A. Schilders, E.J.W. ter Maten,eds. (paper)

S.Holst, A.Jüngel and P.Pietra: Finite element discretizations of semiconductor energy-transport equations , to appear in Oberwolfach Conference Proceedings: Mathematical Modelling, Simulation and Optimization of Integrated Electrical Circuits ,Birkhauser, Basel, 2003. (paper)

S.Holst, A.Jüngel and P.Pietra: An adaptive mixed scheme for energy-transport simulations of field-effect transistors , submitted to SIAM Jour. Scien.Comp.(paper)

N. Ben Abdallah, F.Mehats, P.Pietra, N.Vauchelet: A drift-diffusion subband model for the Double-Gate MESFET, IEEE-NANO Conference on Nanotechnology, Nagoya, Japan (2005). (paper)

F. Brezzi, L. D. Marini, S. Micheletti, P. Pietra, R. Sacco: Stability and Error Analysis of Mixed Finite Volume Methods for Advection Dominated Problems, Computers & Mathematics with Applications, 51 (2006), 681-696. (paper)

SIAM Jour. Appl. Math.

(paper)

P.Pietra and N.Vauchelet: Modeling and simulation of the diffusive transport in a nano-scale Double-Gate MOSFET. Submitted to J. Comput. Phys. (paper)