GAMBA, IRENE M

Irene M Gamba

Professor
Department of Mathematics, Institute for Computational Engineering and Science, Vice-President for Research

W. A. "Tex" Moncrief, Jr. Chair in Computational Engineering and Sciences III

Applied Mathematics, Partial Differential Equations.

gamba@math.utexas.edu

Phone: 512-471-7711

Office Location
RLM 10.166

Postal Address
The University of Texas at Austin
Department of Mathematics, College of Natural Sciences
1 University Station C1200
Austin, TX 78712

Ph.D., University of Chicago (1989)

Research Interests

Applied and Computational analysis, Mathematical and Statistical Physics, non-linear Kinetic and Partial Differential Equations.

Member of the Applied Mathematics Group at The Institute for Computational Engineering and Sciences (ICES)

92- Y.Cheng, I.M. Gamba, Fengyan Li and P.J. Morrison , Discontinuous Galerkin Methods for Vlasov-Maxwell Equations, submitted (2013).

91- I.M. Gamba and R. Srinivasan, Self-similarity in kinetic models of information-exchange processes, submitted (2013).

90- I.M.Gamba, A. Majorana, J.A. Morales and C-W. Shu, A fast approach to Discontinuous Galerkin solvers to Boltzmann-Poisson transport system for full electronic bands and phonon scattering, to appear in Proceedings of IWCE15 (2012),

89- A. Munafo, J.R. Haack, I.M. Gamba and T.E. Magin, High Performance Computing with a Conservative Spectral Boltzmann Solver Investigation of non-equilibrium internal energy excitation in shock waves by means of a spectral-Lagrangian Boltzmann solver, (peer reviewed) to appear in 28th Rarefied Gas Dynamics Conference (2012). AIP Conference Proceedings, (2012).

88- J.R.Haack and I.M. Gamba, High Performance Computing with a Conservative Spectral Boltzmann Solver, (peer reviewed) to appear in 28th Rarefied Gas Dynamics Conference (2012). AIP Conference Proceedings (2012)

87- J.R.Haack and I.M. Gamba, Conservative Deterministic Spectral Boltzmann Solver near the grazing collisions limit, (peer reviewed) to appear in 28th Rarefied Gas Dynamics Conference (2012). AIP Conference Proceedings (2012).

86- Y. He,I.M. Gamba, H-C. Lee, and K. Ren, On the modeling and simulation of semiconductor-electrolyte solar cells, submitted for publication, (2012).

85- R. Alonso, I.M. Gamba and S.H. Tharkabhushaman, Convergence of the Lagrangian based Conservative Spectral method for Space-homogeneous non-linear Boltzmann Equation for hard potentials, submitted for publication, (2012).

84- Y.Cheng, I.M. Gamba and P.J. Morrison, Study of conservation and recurrence of Runge-Kutta discontinuous Galerkin schemes for Vlasov-Poisson systems, To appear in Journal of Scientific Computing (2013) arXiv:1209.6413 [math.AP] .

83- M. Bostan and I.M. Gamba, Impact of strong magnetic fields on collision mechanism for transport of charged particles, Journal Stat. Phys., Vol 147, No.4, August 2012- Online version. arXiv: 1205.2327v1 [math.AP] .

82- R.J. Alonso, J.A. Canizo, I.M. Gamba and C. Mouhot, A new approach to the creation and propagation of exponential moments in the Boltzmann equation, to appear in Comm PDE (2012), preprint at arXiv:1203.2364v1 [math.AP].

81-Y. Cheng and I.M. Gamba, Numerical study of Vlasov-Poisson equations for infinite homogeneous stellar systems, Communications in Nonlinear Science and Numerical Simulation, Vol. 17, Is. 5, pages 2052 - 2061, (2012).

80- N. Ben Abdallah, I.M. Gamba and G. Toscani, On the minimization problem of sub-linear convex functionals, Kinetic Related Models, Vol 4 No.4 pp 857 - 871, (2011).

79- Ricardo Alonso and I.M. Gamba, Gain of integrability for the Boltzmann collisional operator, Kinetic and Related Models, Vol 4, no 1, pages 41 - 51, (2011).

78- Yingda Cheng, I.M. Gamba, A. Majorana, and C-W Shu, Discontinuous Galerkin methods for the Boltzmann-Poisson systems in semiconductor device simulations, AIP Conference Proceedings, v1333 (2011), pp. 890 - 895.

77- Yingda Cheng, I.M. Gamba, A. Majorana, and C-W Shu, Performance of a Discontinuous Galerkin Solvers for Semiconductor Boltzmann Equations, Proceeding of IWCE14, pp.211-214, (2010).

76- Yingda Cheng, I.M. Gamba, A. Majorana, and C-W Shu, A brief survey of the discontinuous Galerkin method for the Boltzmann-Poisson equations, SEMA J. No. 54 , pp. 47 - 64, (2011).

75- Yingda Cheng, Irene M. Gamba, Kui Ren, Recovering doping profiles in semiconductor devices with the Boltzmann-Poisson model, J. Comput. Phys., 230, (2011), pp. 3391-3412.

74- A. Arnold, I.M.Gamba, M.P.Gualdani, S. Mischler, C. Mouhot and C. Sparber; The Wigner-Fokker-Planck equation: Stationary states and large time behavior, Mathematical Models and Methods in Applied Sciences 22 No11, 1250034, 31pp. (2012).

73- R. E. Heath, I. M. Gamba, P. J. Morrison, C. Michler, A discontinuous Galerkin method for the Vlasov-Poisson system, Journal of Computational Physics, Volume 231, Issue 4, 20, February 2012, pp1140 – 1174 (arXiv:1009.3046v2 [physics.plasm-ph]) .

72- A.V. Bobylev and I. M. Gamba, Solutions of the linear Boltzmann equation and some Dirichlet series, Forum Mathematicum, Vol. 24, Issue 2, pp 239 - 251, (2012). Published online: 09/09/2010 DOI:10.1515/FORM.2011.058 (2010).

71- M. Bostan, I.M. Gamba, and T. Goudon, The linear Boltzmann equation with space periodic electric field, Amer. Math. Soc. Transl. (2) Vol 229 pp 51-66 (2010).

70- Yingda Cheng, I.M. Gamba, A. Majorana, and C-W Shu, A Discontinuous Galerkin Solver for Full-Band Boltzmann-Poisson Models, 13th International Workshop on Computational Electronics Proceedings, pp 211-214, (2009).

69- I.M. Gamba, A. Jungel and A. Vasseur , Global existence of solutions to one-dimensional viscous quantum hydrodynamic equations, Journal of Differential Equations, 247, 3117- 3135, (2009).

68- I.M. Gamba and Sri Harsha Tharkabhushaman, Shock and Boundary Structure formation by Spectral-Lagrangian methods for the Inhomogeneous Boltzmann Transport Equation, Jour. Comp. Math, Vol.28, No.4, 2010, pp. 430-460.

67- R. Alonso and I.M.Gamba, A revision on Classical solutions to the Cauchy Boltzmann problem for soft potentials, J. Stat. Phys. 143, no. 4, pp. 740 - 746. (2011)

66- R. Alonso and I.M.Gamba, Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section, Journal of Statistical Physics, V 137, Numbers 5-6, 1147 - 1165 (2009)

65- R. Alonso, E Carneiro and I.M.Gamba, Convolution inequalities for the Boltzmann collision operator, Comm. Math. Physics Volume 298, Number 2, 293-322, 2010.

64- I.M. Gamba, M.P. Gualdani and C. Sparber, A note on the time decay of solutions for the linearized Wigner-Poisson system, Journal Kinetic and Related Models , 2 (2009), no. 1, 181-189. .

63- Yingda Cheng, I.M. Gamba, A. Majorana, and C-W Shu, A discontinuous Galerkin solver for Boltzmann Poisson systems in nano devices, Comput. Methods Appl. Mech. Engrg. 198 (2009), no. 37-40, 3130--3150

62- I.M. Gamba, M.P. Gualdani and R. Sharp, An Adaptable Discontinuous Galerkin Scheme for the Wigner-Fokker-Planck Equation, Commun. Math. Sci. Vol. 7, No. 3 pp. 635-664 (2009).

61- M. Bostan, I. M. Gamba, T. Goudon and A. Vasseur, Boundary Value Problems for the Stationary Vlasov-Boltzmann-Poisson Equation, Indiana University Journal, 59 (2010), no.5, 1629-1660.

60- Yingda Cheng, I.M. Gamba, A. Majorana, and C-W Shu, Discontinuous Galerkin Solver for Boltzmann-Poisson transients, Journal of Computational Electronics, (2008) 7:119-123.

59 - R. Alonso and I.M.Gamba, L1-L∞ Maxwellian bounds for the derivatives of the solution of the homogeneous Boltzmann equation, Journal de Mathematiques Pures et Appliquees, (9) 89 (2008), no. 6, 575—595.

58 - I.M. Gamba and Sri Harsha Tharkabhushaman, Spectral - Lagrangian based methods applied to computation of Non - Equilibrium Statistical States, Journal of Computational Physics 228 (2009) 2012-2036.

57 - Yingda Cheng, Irene M. Gamba, Armando Majorana and Chi-Wang Shu, Discontinuous Galerkin Solver for the Semiconductor Boltzmann Equation, Simulations of Semiconductor Processes And Devices, Vol 12, Springer Wien New York, Edited by T. Grasser and S. Selberherr September 2007; 257-260 (2007).

56 - Yingda Cheng, I.M. Gamba and Jennifer Proft, Positivity-Preserving Discontinuous Galerkin Schemes for Linear Vlasov-Boltzmann Transport Equations, Mathematics of Computation, v81 (2012), pp.153-190.

55- I.M. Gamba, M.P. Gualdani and Ping Zhang, On the blowing up of solutions to the quantum hydrodynamic equations in a bounded domain, Monatshefte Matematik (2009) 157: 37-54.

54 - I.M. Gamba, V. Panferov and C. Villani, Upper Maxwellians bounds for the spatially homogeneous Boltzmann equation, Arch.Rat.Mech.Anal, 194. (2009), 253-282

53 - M.J.Caceres, J.Carrillo, I.M.Gamba, A.Majorana and C.W.Shu, Deterministic kinetic solvers for charged particle transport in semiconductor devices, Transport Phenomena and Kinetic Theory, Applications to Gases, Semiconductors, Photons, and Biological Systems Series: Modeling and Simulation in Science, Engineering and Technology. Cercignani, Carlo and Gabetta, Ester (Eds.) (2007).


52 - M.J.Caceres, J.Carrillo, I.M.Gamba, A.Majorana and C.W.Shu, DSMC vs WENO-BTE: a Double Gate MOSFET Example. Journal of Computational Electronics, Volume 5, Number 4-December (2006) 471-474.

51 - A.V. Bobylev, C. Cercignani and I. M. Gamba, On the self-similar asymptotics for generalized non-linear kinetic Maxwell models, Commun. Mathematical Physics 291, 599 - 644 (2009). (original version at arXiv:math-ph/0608035)

50 - A.V. Bobylev, C. Cercignani and I. M. Gamba, Generalized kinetic Maxwell models of granular gases; Mathematical models of granular matter Series: Lecture Notes in Mathematics Vol.1937, Springer, G. Capriz, P. Giovine and P. M. Mariano (Eds.) (2008) ISBN: 978-3-540-78276-6 .

49 - A.V. Bobylev and I. M. Gamba, Boltzmann equations for mixtures of Maxwell gases: exact solutions and power like tails, J. Stat. Phys. 124, no. 2-4, 497--516. (2006).

48 - J.A. Carrillo, I.M. Gamba, A. Majorana and C.W. Shu, 2D non-stationary Boltzmann- Poisson Systems: DSMC versus A WENO-Boltzmann scheme, J. Comput. Phys. 214 (2006), no.1, 55-80.

47 - Jing Shi, I.M. Gamba, A Unitary Hermite Spectral Method for Quantum Liouville-von Neumann Equation, Preprint (2005).

46 - I.M. Gamba, S. Rjasanow and W.Wagner, Direct simulation of the uniformly heated granular Boltzmann equation, Math. Comput. Modelling 42 (2005), no. 5-6, 683--700.

45 - A.V. Bobylev, I.M. Gamba and V. Panferov, Moment inequalities and high-energy tails for Boltzmann equations with inelastic interactions, J. Statist. Phys. 116, no. 5-6, 1651-1682.(2004).

44 - I.M. Gamba, V. Panferov and C. Villani, On the Boltmann Equation for diffusively excited granular media, Commun. Math. Phys. 246, 503-541 (2004).

43 - N. Ben Abdallah, I.M. Gamba and A. Klar, The Milne problem for high field kinetic equations, SIAM J. Appl. Math. Vol.64 No.5, pp. 1709-1736 (2004).

42 - J.A. Carrillo, I.M. Gamba, A. Majorana and C.W. Shu, A direct solver for 2D nonstationary Boltzmann-Poisson Systems for Semiconductor Devices: A MESFET simulation by WENO-Boltzmann schemes, Journal of Computational Electronics, 2: 375-380 (2005).

41 - Luis Caffarelli, Valentino Crespi, George Cybenko, Daniela Rus, Irene M. Gamba, Stochastic Distributed Algorithms for Target Surveillance, Proceedings of Intelligent Systems and Design Applications (ISDA2003), Tulsa, Oklahoma, August, 2003.

40 - J.A. Carrillo, I.M. Gamba, A. Majorana and C.W. Shu, A WENO-solver transients of Boltzmann-Poisson system for semiconductor devices. Performance and Monte Carlo comparisons, Journal of Computational Physics, Vol 184, no. 2, 498-525, (2003).

39 - Gamba, V. Panferov and C. Villani, On the inelastic Boltzmann equation with diffusive forcing. Nonlinear problems in mathematical physics and related topics, II, In Honor of Professor O.A.Ladyzhenskaya 179-192, Int. Math. Ser. (N. Y.), 2, Kluwer/Plenum, New York,(2002).

38 - K. Suzanne Barber, Irene M. Gamba, and Cheryl E. Martin. Representing and Analyzing Adaptive Decision Making Frameworks. Agent Autonomy, Kluwer series: Multi-Agent Systems, Artificial Societies, and Simulated Organizations, Gerhard Weiss (editor), Chapter 3, (2003). (Workshop on Autonomy Oriented Computation (AOC) (invited) 5th International Conference on Autonomous Agents, pp. 12-20, May 28-June 1, 2001, Montreal, Canada.)

37 - K. Suzanne Barber, Irene M. Gamba, and Cheryl E. Martin. Analysis of Adaptive Decision-Making Frameworks: Motivation for Adjusting Autonomy through Decision-Making Control. Proceedings for the IJCAI-01 Workshop on Autonomy, Delegation, and Control: Interacting with Autonomous Agents. pp. 9-13, August 4-10, (2001), Seattle, WA.

36 - J.A. Carrillo, I.M. Gamba, A. Majorana and C.W. Shu, A WENO-solver for the 1D non-stationary Boltzmann-Poisson system for semiconductor devices. Journal of Computational Electronics, v1 (2002), pp.365-370.

35 - N. Ben Abdallah, P. Degond and I. Gamba, Hybrid-quantum-kinetic models for the coupling kinetic and quantum effect, J. Math. Phys. 43 (2002), no. 1, 1-24.(2002).

34 - I.M. Gamba and A. Jungel, Asymptotic limits for Quantum Trajectory Models, Comm. Partial Differential Equations 27 (2002), no. 3-4, 669-691.(April, 2002).

33 - J.A. Carrillo, I.M. Gamba, O. Muscato and C.W. Shu, Comparison of Monte Carlo and deterministic simulations of a silicon diode, Simulation of Transport in Transition Regimes, 75-84, IMA Vol. Math. Appl., 135, Springer, New York, 2004 (Minneapolis, MN, 2000),

32 - A.V. Bobylev, J.A. Carrillo and I.M. Gamba, Erratum on: "On some properties of kinetic and hydrodynamic equations for inelastic interactions", Journal Stat. Phys., vol. 103, no. 5-6, 1137 - 1138 (2001).

31 - M.A. Anile, J.A. Carrillo, I.M. Gamba and C.W. Shu, Approximation of the BTE by a relaxation-time operator: simulations for a 50nm-channel Si diode, VLSI Design Journal 13, 349-354 (2001)

30 - C. Cercignani, I.M. Gamba, C.L. Levermore, A Drift-Collision Balance asymptotic for a Boltzmann-Poisson System in Bounded Domains, SIAM J. Appl. Math., Vol 61, No. 6, pp 1932-1958, (2001).

29 - I.M. Gamba and A. Jungel, Positive solutions to singular second and third order differential equations for quantum fluids, Arch. Ration. Mech. Anal. 156, no.3,183-203 (2001).

28 - P. Amster, I.M. Gamba, M.C. Mariani, and P. Varela, Solutions to transonic nonisentropic charged transport hydrodynamic systems in bounded domains, preprint (2000)

27 - J.A. Carrillo, C. Cercignani and I.M. Gamba, Steady states of a Boltzmann equation for driven granular media, Phys. Rev. E (3) 62 (2000), no. 6, part A, 7700-7707. 27.

26 - N. Ben Abdallah, P. Degond and I. Gamba, Inflow boundary conditions for the time dependent one-dimensional Schroedinger equation, C.R.Acad. Sci. Paris Sr. I Math. 331 (2000), no.12, 1023-1028

25 - C. Cercignani, I. Gamba, J. Jerome and C.-W. Shu, A domain decomposition method: a simulation study, Proceedings of 1998 Sixth International Workshop on Computational Electronics (IWCE-6), Osaka University, Japan, October 19-21, 1998, IEEE Catalog Number 98EX116, pp.174-177 (1998).

24 - J.A. Carrillo, I.M. Gamba and C.W. Shu, Computational macroscopic approximations to the 1-D relaxation-time kinetic system for semiconductors, Physica D 146, 289-306 (2000).

23 - Arnold , J.A. Carrillo, I. Gamba and Chi-Wang Shu, Low and High Field Scaling Limits for the Vlasov- and Wigner-Poisson-Fokker-Planck Systems, Transp. Theory Stat. Phys 30 (2&3), 121-153 (2001).

22 - A.V. Bobylev, J.A. Carrillo and I.M. Gamba, On some properties of kinetic and hydrodynamic equations for inelastic interactions, Journal Stat. Phys., vol. 98, no. 3-4, 743-773, (2000).

21 - I.M. Gamba, Milne Problem for strong force scaling, Nonlinear partial differential equations (Evanston, IL, 1998), 127-132, Contemp. Math., 238, Amer. Math. Soc., Providence, RI, (1999).

20 - C. Cercignani, I.M. Gamba, J. Jerome and C-W Shu, A Domain Decomposition Method for Silicon Devices, Transport Theory and Statis. Phys., vol. 29, (3-5), 525-536 (2000).

19 - C. Cercignani, I.M. Gamba, J. Jerome and C-W Shu, Device Benchmark Comparisons via Kinetic, Hydrodynamic, and High-Field Models, Computer Methods in Applied Mechanics and Engineering, 381-392 (2000).

18 - I.M. Gamba, R. Rosales and E. Tabak, Constraints for formation of singularities for the small disturbance transonic flow equations, Comm. Pure Appl. Math, 52 no. -6, 763-779 (1999).

17 - C. Cercignani, I.M. Gamba, J. Jerome and C-W Shu, Applicability of the high field model: A preliminary numerical study, Proceedings of Fifth International Workshop on Computational Electronics (1997), Notre Dame, Indiana. VLSI DESIGN, vol. 8 (1-4), 135-141 (1998).

16 - C. Cercignani, I.M. Gamba, J. Jerome and C-W Shu, Applicability of the high field model: An analytical study via asymptotic parameters defining domain decomposition, Proceedings of Fifth International Workshop on Computational Electronics (1997), Notre Dame, Indiana. VLSI DESIGN, vol. 8 (1?4), 275-282 (1998).

15 - I.M. Gamba, Higher order asymptotic boundary conditions for an oxide region in a semiconductor device, Wavelet Theory and Harmonic Analysis in Applied Sciences, edited by C.E. D'Attellis and E.M. Fernandez-Berdaguer, Birkhauser, 1997 (ISBN 0-8176-3953-5, ISBN 3-7643-3953-5) 301-313 (1997).

14 - I.M. Gamba and C.S. Morawetz, Viscous approximation to transonic gas dynamics: flow past profiles and charged-particle systems, Modeling and Computation for Applications in Mathematics, Science and Engineering (Evanston, Il, 1996), Clarendon Press, Oxford, 81-102, (1998).

13 - C. Cercignani, I.M. Gamba and C.D. Levermore, High field approximations to a Boltzmann-Poisson system boundary conditions in a semiconductor, Applied Math Letters, vol. 10 (4), 111-118, (1997).

12 - I.M. Gamba, Sharp uniform speed bounds for steady potential fluid-Poisson systems, Proceedings of the Royal Academy of Edinburgh, vol. 127A, 479-516 (1997).

11 - I.M. Gamba, Steady Potential Fluid-Poisson systems: Theoretical results in 2-dimensional geometries, Proceedings of ICIAM 95 - Applied Analysis Volume (1997)

10 - I.M. Gamba and C.S. Morawetz, A viscous approximation for a 2D steady semiconductor or transonic gas dynamic flow: Existence theorem for potential flow, Communications in Pure and Applied Mathematics, vol. 49 (10) 999-1049 (1996).

9 - I.M. Gamba, An existence and uniqueness result for a nonlinear 2-dimensional elliptic boundary value problem, Communications in Pure and Applied Mathematics, vol. XLVIII, 669-689 (1995).

8 - I.M. Gamba, Viscosity approximating solutions to ODE systems that admit shocks, and their limits, Advances in Applied Mathematics, vol. 15, 129-182, (1994).

7 - I.M. Gamba, Boundary layer formation for viscosity approximations of transonic flow, Physics of Fluids A., vol. 4(3), 486-490 (1992).

6 - I.M. Gamba, Stationary transonic solutions for a one-dimensional hydrodynamic model for semiconductors, Comm. Partial Differential Equations, vol. 17 (3,9), 553-577 (1992).

5 - I.M. Gamba, Asymptotic boundary conditions for an oxide region in a semiconductor device, Asymptotic Analysis Journal, vol. 7, 37-48 (1993).

4 - I.M. Gamba, Behavior of the potential at the pn-Junction for a model in semiconductor theory,
Appl. Math. Lett., vol. 3, 59-63 (1990).

3 - I.M. Gamba, Asymptotic behavior at the boundary of a semiconductor device in two space dimensions, (based on the PhD thesis dissertation), (Istituto di Analisi Numerica del C.N.R. Pub.N.740. Pavia, Italy (1990)). Ann. di Mat. Pura App. (IV) Vol. CLXIII, 43-91, (1993).

2 - I.M. Gamba and M.C.J. Squef Simulation of the transient behavior of a one dimensional semiconductor device II, SIAM of J. Numer. Anal., vol. 2, 539-552 (1989).

1 - J. Douglas Jr., I.M. Gamba and M.C.J. Squeff, Simulation of the transient behavior of a one dimensional semiconductor device, Mat. Apl. Comput., vol. 5, 103-122 (1986).
  • Japan Society for the Promotion of Science (JSPS) fellowship at Kyoto University, Japan, March 2013.
  • Inaugural class of Fellows of the AMS 2013.
  • ICES Distinguished Research Award for 2012.
  • SIAM Fellow class 2012.
  • Moncrief Grand Challenge Award, 2008-2009.
  • Joe B. and Louise Cook Professorship in Mathematics, 2007 to 2011.
  • XV David Alcaraz Spinola Lecture Award, Universidad Autonoma de Mexico, Ciudad de Mexico, October 2005.
  • NSF Mathematical Science Postdoctoral Research Fellow, 1992-1994.