Alonso, Ricardo J.; Gamba, Irene M. The Boltzmann equation for hard potentials with integrable angular transition: Coerciveness, exponential tails rates, and Lebesgue integrability. arXiv:2211.09188 Preprint, arXiv:2211.09188 [math-ph] (2022). MSC: 35Q20 82C22 82C40 45G05 40H05 BibTeX Cite \textit{R. J. Alonso} and \textit{I. M. Gamba}, ``The Boltzmann equation for hard potentials with integrable angular transition: Coerciveness, exponential tails rates, and Lebesgue integrability'', Preprint, arXiv:2211.09188 [math-ph] (2022) Full Text: arXiv OA License
Gamba, Irene M.; Jin, Shi; Liu, Liu Asymptotic-preserving schemes for two-species binary collisional kinetic system with disparate masses. I: Time discretization and asymptotic analysis. (English) Zbl 1433.35211 Commun. Math. Sci. 17, No. 5, 1257-1289 (2019). MSC: 35Q20 82D10 65M99 35Q84 76P05 82C31 76X05 35B40 82C40 65M06 PDFBibTeX XMLCite \textit{I. M. Gamba} et al., Commun. Math. Sci. 17, No. 5, 1257--1289 (2019; Zbl 1433.35211) Full Text: DOI arXiv
Zhang, Chenglong; Gamba, Irene M. A conservative discontinuous Galerkin solver for the space homogeneous Boltzmann equation for binary interactions. (English) Zbl 1403.65079 SIAM J. Numer. Anal. 56, No. 5, 3040-3070 (2018). MSC: 65M60 65Y05 45K05 82B40 65M15 65F50 35Q20 PDFBibTeX XMLCite \textit{C. Zhang} and \textit{I. M. Gamba}, SIAM J. Numer. Anal. 56, No. 5, 3040--3070 (2018; Zbl 1403.65079) Full Text: DOI
Morales Escalante, José A.; Gamba, Irene M. Galerkin methods for Boltzmann-Poisson transport with reflection conditions on rough boundaries. (English) Zbl 1395.65083 J. Comput. Phys. 363, 302-328 (2018). MSC: 65M60 65Z05 35Q60 82D37 PDFBibTeX XMLCite \textit{J. A. Morales Escalante} and \textit{I. M. Gamba}, J. Comput. Phys. 363, 302--328 (2018; Zbl 1395.65083) Full Text: DOI arXiv
Zhang, Chenglong; Gamba, Irene M. Spectral Gap Computations for Linearized Boltzmann Operators. arXiv:1807.09868 Preprint, arXiv:1807.09868 [math-ph] (2018). MSC: 65M60 65Y05 45P05 45C05 47A75 82B40 BibTeX Cite \textit{C. Zhang} and \textit{I. M. Gamba}, ``Spectral Gap Computations for Linearized Boltzmann Operators'', Preprint, arXiv:1807.09868 [math-ph] (2018) Full Text: arXiv OA License
Morales-Escalante, José; Gamba, Irene M.; Cheng, Yingda; Majorana, Armando; Shu, Chi-Wang; Chelikowsky, James Discontinuous Galerkin deterministic solvers for a Boltzmann-Poisson model of hot electron transport by averaged empirical pseudopotential band structures. (English) Zbl 1439.82062 Comput. Methods Appl. Mech. Eng. 321, 209-234 (2017). MSC: 82M10 65M60 45K05 82C70 PDFBibTeX XMLCite \textit{J. Morales-Escalante} et al., Comput. Methods Appl. Mech. Eng. 321, 209--234 (2017; Zbl 1439.82062) Full Text: DOI arXiv
Harmon, Michael; Gamba, Irene M.; Ren, Kui Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells. (English) Zbl 1373.82101 J. Comput. Phys. 327, 140-167 (2016). MSC: 82D37 65M60 PDFBibTeX XMLCite \textit{M. Harmon} et al., J. Comput. Phys. 327, 140--167 (2016; Zbl 1373.82101) Full Text: DOI arXiv
Gamba, Irene M.; Haack, Jeffrey R.; Motsch, Sebastien Spectral method for a kinetic swarming model. (English) Zbl 1349.76682 J. Comput. Phys. 297, 32-46 (2015). MSC: 76M28 78M12 65M70 76P05 82C22 PDFBibTeX XMLCite \textit{I. M. Gamba} et al., J. Comput. Phys. 297, 32--46 (2015; Zbl 1349.76682) Full Text: DOI
Bobylev, Alexander; Gamba, Irene; Potapenko, Irina On some properties of the Landau kinetic equation. (English) Zbl 1333.35151 J. Stat. Phys. 161, No. 6, 1327-1338 (2015). MSC: 35Q20 82C31 35Q84 82C40 82D10 82C80 PDFBibTeX XMLCite \textit{A. Bobylev} et al., J. Stat. Phys. 161, No. 6, 1327--1338 (2015; Zbl 1333.35151) Full Text: DOI
Gamba, Irene M.; Haack, Jeffrey R. A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit. (English) Zbl 1349.82080 J. Comput. Phys. 270, 40-57 (2014). MSC: 82C80 76M22 65M70 76P05 82C31 82D10 PDFBibTeX XMLCite \textit{I. M. Gamba} and \textit{J. R. Haack}, J. Comput. Phys. 270, 40--57 (2014; Zbl 1349.82080) Full Text: DOI arXiv
Munafò, Alessandro; Haack, Jeffrey R.; Gamba, Irene M.; Magin, Thierry E. A spectral-Lagrangian Boltzmann solver for a multi-energy level gas. (English) Zbl 1349.76720 J. Comput. Phys. 264, 152-176 (2014). MSC: 76M28 65M75 76P05 82C80 82C40 PDFBibTeX XMLCite \textit{A. Munafò} et al., J. Comput. Phys. 264, 152--176 (2014; Zbl 1349.76720) Full Text: DOI arXiv
Cheng, Yingda; Gamba, Irene M.; Morrison, Philip J. Study of conservation and recurrence of Runge-Kutta discontinuous Galerkin schemes for Vlasov-Poisson systems. (English) Zbl 1281.82028 J. Sci. Comput. 56, No. 2, 319-349 (2013). Reviewer: Iván Abonyi (Budapest) MSC: 82D10 76W05 82-08 35Q83 PDFBibTeX XMLCite \textit{Y. Cheng} et al., J. Sci. Comput. 56, No. 2, 319--349 (2013; Zbl 1281.82028) Full Text: DOI arXiv
Arnold, Anton; Gamba, Irene M.; Gualdani, Maria Pia; Mischler, Stéphane; Mouhot, Clement; Sparber, Christof The Wigner-Fokker-Planck equation: stationary states and large time behavior. (English) Zbl 1253.82065 Math. Models Methods Appl. Sci. 22, No. 11, 1250034, 31 p. (2012). MSC: 82C31 82C10 35S10 74H40 81Q15 PDFBibTeX XMLCite \textit{A. Arnold} et al., Math. Models Methods Appl. Sci. 22, No. 11, Article ID 1250034, 31 p. (2012; Zbl 1253.82065) Full Text: DOI arXiv
Heath, R. E.; Gamba, I. M.; Morrison, P. J.; Michler, C. A discontinuous Galerkin method for the Vlasov-Poisson system. (English) Zbl 1244.82081 J. Comput. Phys. 231, No. 4, 1140-1174 (2012). Reviewer: Iván Abonyi (Budapest) MSC: 82D10 35Q83 76W05 82-08 65M60 PDFBibTeX XMLCite \textit{R. E. Heath} et al., J. Comput. Phys. 231, No. 4, 1140--1174 (2012; Zbl 1244.82081) Full Text: DOI arXiv
Cheng, Yingda; Gamba, Irene M.; Proft, Jennifer Positivity-preserving discontinuous Galerkin schemes for linear Vlasov-Boltzmann transport equations. (English) Zbl 1233.82036 Math. Comput. 81, No. 277, 153-190 (2012). MSC: 82C70 76P05 65M60 35Q20 35Q83 82-08 PDFBibTeX XMLCite \textit{Y. Cheng} et al., Math. Comput. 81, No. 277, 153--190 (2012; Zbl 1233.82036) Full Text: DOI
Gamba, Irene M.; Haack, Jeffrey R. High Performance Computing with a Conservative Spectral Boltzmann Solver. arXiv:1211.0540 Preprint, arXiv:1211.0540 [math.NA] (2012). MSC: 65M08 65M70 82B40 82B80 65Y05 BibTeX Cite \textit{I. M. Gamba} and \textit{J. R. Haack}, ``High Performance Computing with a Conservative Spectral Boltzmann Solver'', Preprint, arXiv:1211.0540 [math.NA] (2012) Full Text: arXiv OA License
Gamba, Irene M.; Haack, Jeffrey R. Conservative Deterministic Spectral Boltzmann Solver Near the Grazing Collisions Limit. arXiv:1211.0327 Preprint, arXiv:1211.0327 [math.NA] (2012). MSC: 65M70 65M08 82C40 BibTeX Cite \textit{I. M. Gamba} and \textit{J. R. Haack}, ``Conservative Deterministic Spectral Boltzmann Solver Near the Grazing Collisions Limit'', Preprint, arXiv:1211.0327 [math.NA] (2012) Full Text: arXiv OA License
Cheng, Yingda; Gamba, Irene M.; Majorana, Armando; Shu, Chi-Wang A brief survey of the discontinuous Galerkin method for the Boltzmann-Poisson equations. (English) Zbl 1242.65202 S\(\vec{\text{e}}\)MA J. 54, 47-64 (2011). MSC: 65M60 35Q20 82-08 82D37 PDFBibTeX XMLCite \textit{Y. Cheng} et al., S\(\vec{\text{e}}\)MA J. 54, 47--64 (2011; Zbl 1242.65202) Full Text: DOI
Gamba, Irene M.; Tharkabhushanam, Sri Harsha Shock and boundary structure formation by spectral-Lagrangian methods for the inhomogeneous Boltzmann transport equation. (English) Zbl 1228.76138 J. Comput. Math. 28, No. 4, 430-460 (2010). MSC: 76P05 82C70 82C40 65M70 76M22 PDFBibTeX XMLCite \textit{I. M. Gamba} and \textit{S. H. Tharkabhushanam}, J. Comput. Math. 28, No. 4, 430--460 (2010; Zbl 1228.76138) Full Text: DOI Link
Cheng, Yingda; Gamba, Irene M.; Majorana, Armando; Shu, Chi-Wang A discontinuous Galerkin solver for Boltzmann-Poisson systems in nano-devices. (English) Zbl 1229.82005 Comput. Methods Appl. Mech. Eng. 198, No. 37-40, 3130-3150 (2009). MSC: 82-08 82D37 78A35 PDFBibTeX XMLCite \textit{Y. Cheng} et al., Comput. Methods Appl. Mech. Eng. 198, No. 37--40, 3130--3150 (2009; Zbl 1229.82005) Full Text: DOI arXiv
Gamba, Irene M.; Gualdani, Maria Pia; Sharp, Richard W. An adaptable discontinuous Galerkin scheme for the Wigner-Fokker-Planck equation. (English) Zbl 1185.65180 Commun. Math. Sci. 7, No. 3, 635-664 (2009). Reviewer: Qin Mengzhao (Beijing) MSC: 65M60 65M12 65M15 35Q84 82C31 PDFBibTeX XMLCite \textit{I. M. Gamba} et al., Commun. Math. Sci. 7, No. 3, 635--664 (2009; Zbl 1185.65180) Full Text: DOI
Gamba, Irene M.; Tharkabhushanam, Sri Harsha Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states. (English) Zbl 1159.82320 J. Comput. Phys. 228, No. 6, 2012-2036 (2009). MSC: 82C70 82C40 76P05 65T50 PDFBibTeX XMLCite \textit{I. M. Gamba} and \textit{S. H. Tharkabhushanam}, J. Comput. Phys. 228, No. 6, 2012--2036 (2009; Zbl 1159.82320) Full Text: DOI arXiv
Gamba, Irene M. (ed.); Rjasanow, Sergej (ed.); Wagner, Wolfgang (ed.) Mini-workshop: Numerics for kinetic equations. Abstracts from the mini-workshop held November 16th – November 22nd, 2008. (English) Zbl 1177.76008 Oberwolfach Rep. 5, No. 4, 2943-2984 (2008). MSC: 76-06 76P05 82C40 65C05 00B05 PDFBibTeX XMLCite \textit{I. M. Gamba} (ed.) et al., Oberwolfach Rep. 5, No. 4, 2943--2984 (2008; Zbl 1177.76008) Full Text: DOI Link
Cáceres, M. J.; Carrillo, J. A.; Gamba, I. M.; Majorana, A.; Shu, C.-W. Deterministic kinetic solvers for charged particle transport in semiconductor devices. (English) Zbl 1203.82109 Cercignani, Carlo (ed.) et al., Transport phenomena and kinetic theory. Applications to gases, semiconductors, photons, and biological systems. Boston, MA: Birkhäuser (ISBN 978-0-8176-4489-5/hbk). Modeling and Simulation in Science, Engineering and Technology, 151-171 (2007). MSC: 82D37 82C70 78A15 76P05 82C80 PDFBibTeX XMLCite \textit{M. J. Cáceres} et al., in: Transport phenomena and kinetic theory. Applications to gases, semiconductors, photons, and biological systems. Boston, MA: Birkhäuser. 151--171 (2007; Zbl 1203.82109)
Carrillo, José A.; Gamba, Irene M.; Majorana, Armando; Shu, Chi-Wang 2D semiconductor device simulations by WENO-Boltzmann schemes: efficiency, boundary conditions and comparison to Monte Carlo methods. (English) Zbl 1098.82033 J. Comput. Phys. 214, No. 1, 55-80 (2006). Reviewer: Oleg A. Sinkevich (Moskva) MSC: 82D37 82C70 82-08 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., J. Comput. Phys. 214, No. 1, 55--80 (2006; Zbl 1098.82033) Full Text: DOI
Gamba, I. M.; Rjasanow, S.; Wagner, W. Direct simulation of the uniformly heated granular Boltzmann equation. (English) Zbl 1088.35049 Math. Comput. Modelling 42, No. 5-6, 683-700 (2005). MSC: 35Q35 76T25 76P05 74E20 82C80 PDFBibTeX XMLCite \textit{I. M. Gamba} et al., Math. Comput. Modelling 42, No. 5--6, 683--700 (2005; Zbl 1088.35049) Full Text: DOI
Ben Abdallah, N.; Gamba, I. M.; Klar, Axel The Milne problem for high field kinetic equations. (English) Zbl 1126.82009 SIAM J. Appl. Math. 64, No. 5, 1709-1736 (2004). MSC: 82B40 82C40 82C80 PDFBibTeX XMLCite \textit{N. Ben Abdallah} et al., SIAM J. Appl. Math. 64, No. 5, 1709--1736 (2004; Zbl 1126.82009) Full Text: DOI
Carrillo, Jose A.; Gamba, Irene M.; Muscato, Orazio; Shu, Chi-Wang Comparison of Monte Carlo and deterministic simulations of a silicon diode. (English) Zbl 1041.82524 Ben Abdallah, Naoufel (ed.) et al., Transport in transition regimes. Papers presented at the IMA workshops “Dispersive corrections to transport equations”, May 1–5, 2000, “Simulation of transport in transition regimes”, May 22–26, 2000, and “Multiscale models for surface evolution and reacting flows”, June 5–9, 2000, Minneapolis, MN, USA. New York, NY: Springer (ISBN 0-387-40495-3/hbk). IMA Vol. Math. Appl. 135, 75-84 (2004). MSC: 82C70 82D37 65C05 65M06 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., IMA Vol. Math. Appl. 135, 75--84 (2004; Zbl 1041.82524)
Carrillo, José A.; Gamba, Irene M.; Majorana, Armando; Shu, Chi-Wang A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: Performance and comparisons with Monte Carlo methods. (English) Zbl 1034.82063 J. Comput. Phys. 184, No. 2, 498-525 (2003). MSC: 82D37 82-08 82C40 76P05 76M20 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., J. Comput. Phys. 184, No. 2, 498--525 (2003; Zbl 1034.82063) Full Text: DOI
Carrillo, Jose A.; Gamba, Irene M.; Shu, Chi-Wang Computational macroscopic approximations to the one-dimensional relaxation-time kinetic system for semiconductors. (English) Zbl 0976.82053 Physica D 146, No. 1-4, 289-306 (2000). MSC: 82D37 82C40 35Q99 76P05 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., Physica D 146, No. 1--4, 289--306 (2000; Zbl 0976.82053) Full Text: DOI
Cercignani, Carlo; Gamba, Irene M.; Jerome, Joseph W.; Shu, Chi-Wang A domain decomposition method for Silicon devices. (English) Zbl 1028.82021 Transp. Theory Stat. Phys. 29, No. 3-5, 525-536 (2000). MSC: 82C80 82C40 76P05 82D37 65M55 PDFBibTeX XMLCite \textit{C. Cercignani} et al., Transp. Theory Stat. Phys. 29, No. 3--5, 525--536 (2000; Zbl 1028.82021) Full Text: DOI
Ben Abdallah, Naoufel; Degond, Pierre; Gamba, Irène Inflow boundary conditions for the time dependent one-dimensional Schrödinger equation. (English. Abridged French version) Zbl 1158.35344 C. R. Acad. Sci., Paris, Sér. I, Math. 331, No. 12, 1023-1028 (2000). MSC: 35J10 81Q20 35Q40 82D10 PDFBibTeX XMLCite \textit{N. Ben Abdallah} et al., C. R. Acad. Sci., Paris, Sér. I, Math. 331, No. 12, 1023--1028 (2000; Zbl 1158.35344) Full Text: DOI