Li, Yachun; Peng, Yue-Jun; Zhao, Liang Convergence rates in zero-relaxation limits for Euler-Maxwell and Euler-Poisson systems. (English. French summary) Zbl 1480.35331 J. Math. Pures Appl. (9) 154, 185-211 (2021). MSC: 35Q35 35Q60 35B25 35B10 35B65 35K45 35L45 76X05 78A25 82D37 PDF BibTeX XML Cite \textit{Y. Li} et al., J. Math. Pures Appl. (9) 154, 185--211 (2021; Zbl 1480.35331) Full Text: DOI OpenURL
Alì, Giuseppe; Rotundo, Nella Existence and uniqueness of solution for multidimensional parabolic partial differential-algebraic equations arising in semiconductor modeling. (English) Zbl 1471.35286 Math. Methods Appl. Sci. 44, No. 7, 6117-6142 (2021). MSC: 35R02 34A09 35K51 35K59 82D37 94C05 PDF BibTeX XML Cite \textit{G. Alì} and \textit{N. Rotundo}, Math. Methods Appl. Sci. 44, No. 7, 6117--6142 (2021; Zbl 1471.35286) Full Text: DOI OpenURL
Glitzky, Annegret; Liero, Matthias; Nika, Grigor An existence result for a class of electrothermal drift-diffusion models with Gauss-Fermi statistics for organic semiconductors. (English) Zbl 1460.35127 Anal. Appl., Singap. 19, No. 2, 275-304 (2021). MSC: 35J57 35R05 35D30 78A35 PDF BibTeX XML Cite \textit{A. Glitzky} et al., Anal. Appl., Singap. 19, No. 2, 275--304 (2021; Zbl 1460.35127) Full Text: DOI OpenURL
Kantner, Markus; Koprucki, Thomas Non-isothermal Scharfetter-Gummel scheme for electro-thermal transport simulation in degenerate semiconductors. (English) Zbl 1471.65175 Klöfkorn, Robert (ed.) et al., Finite volumes for complex applications IX – methods, theoretical aspects, examples. FVCA 9, Bergen, Norway, June 15–19, 2020. In 2 volumes. Volume I and II. Cham: Springer. Springer Proc. Math. Stat. 323, 173-182 (2020). Reviewer: Hongliang Li (Chengdu) MSC: 65N08 35K05 35K08 35Q79 35Q82 80M12 82B35 82D37 81V74 PDF BibTeX XML Cite \textit{M. Kantner} and \textit{T. Koprucki}, Springer Proc. Math. Stat. 323, 173--182 (2020; Zbl 1471.65175) Full Text: DOI arXiv OpenURL
Glitzky, Annegret; Liero, Matthias Instationary drift-diffusion problems with Gauss-Fermi statistics and field-dependent mobility for organic semiconductor devices. (English) Zbl 1431.35206 Commun. Math. Sci. 17, No. 1, 33-59 (2019). Reviewer: Guy Jumarie (Montréal) MSC: 35Q82 35D30 82D37 35B45 35K20 35K55 78A35 PDF BibTeX XML Cite \textit{A. Glitzky} and \textit{M. Liero}, Commun. Math. Sci. 17, No. 1, 33--59 (2019; Zbl 1431.35206) Full Text: DOI OpenURL
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 PDF BibTeX XML Cite \textit{M. Harmon} et al., J. Comput. Phys. 327, 140--167 (2016; Zbl 1373.82101) Full Text: DOI arXiv OpenURL
Yamamoto, Masakazu; Sugiyama, Yuusuke Asymptotic expansion of solutions to the drift-diffusion equation with fractional dissipation. (English) Zbl 1381.35235 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 141, 57-87 (2016). MSC: 35R11 35B30 35B33 35C20 35K58 35M31 78A35 82D37 PDF BibTeX XML Cite \textit{M. Yamamoto} and \textit{Y. Sugiyama}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 141, 57--87 (2016; Zbl 1381.35235) Full Text: DOI OpenURL
Jüngel, Ansgar; Negulescu, Claudia; Shpartko, Polina Bounded weak solutions to a matrix drift-diffusion model for spin-coherent electron transport in semiconductors. (English) Zbl 1396.35029 Math. Models Methods Appl. Sci. 25, No. 5, 929-958 (2015). MSC: 35K51 82D37 35A01 35A02 35D30 PDF BibTeX XML Cite \textit{A. Jüngel} et al., Math. Models Methods Appl. Sci. 25, No. 5, 929--958 (2015; Zbl 1396.35029) Full Text: DOI arXiv OpenURL
Alì, Giuseppe; Bartel, Andreas; Rotundo, Nella Index-2 elliptic partial differential-algebraic models for circuits and devices. (English) Zbl 1330.35004 J. Math. Anal. Appl. 423, No. 2, 1348-1369 (2015). MSC: 35A01 78A35 35J57 35J62 PDF BibTeX XML Cite \textit{G. Alì} et al., J. Math. Anal. Appl. 423, No. 2, 1348--1369 (2015; Zbl 1330.35004) Full Text: DOI OpenURL
Lakhdara, Maya; Latreche, Saïda; Gontrand, Christian Mathematical approach and optimisation of nanometric base thickness for a SiGeC HBT dedicated to radiofrequency applications. (English) Zbl 1322.78017 J. Comput. Appl. Math. 259, Part B, 925-936 (2014). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 78M50 78M20 82D37 65F10 PDF BibTeX XML Cite \textit{M. Lakhdara} et al., J. Comput. Appl. Math. 259, Part B, 925--936 (2014; Zbl 1322.78017) Full Text: DOI OpenURL
Bensegueni, Rachida; Latreche, Saida Numerical solution of drift diffusion equations using 2D finite difference method: application to a strained MOSFET device. (English) Zbl 1285.82050 Univers. J. Math. Math. Sci. 4, No. 1, 119-133 (2013). Reviewer: Alexander Mikhajlovich Blokhin (Novosibirsk) MSC: 82D37 82-08 65N06 65F10 PDF BibTeX XML Cite \textit{R. Bensegueni} and \textit{S. Latreche}, Univers. J. Math. Math. Sci. 4, No. 1, 119--133 (2013; Zbl 1285.82050) Full Text: Link OpenURL
Jüngel, Ansgar; Pinnau, René; Röhrig, Elisa Existence analysis for a simplified transient energy-transport model for semiconductors. (English) Zbl 1275.35124 Math. Methods Appl. Sci. 36, No. 13, 1701-1712 (2013). MSC: 35K59 35K20 35Q70 82D37 35K51 PDF BibTeX XML Cite \textit{A. Jüngel} et al., Math. Methods Appl. Sci. 36, No. 13, 1701--1712 (2013; Zbl 1275.35124) Full Text: DOI arXiv OpenURL
Hinze, M.; Kunkel, M. Residual based sampling in POD model order reduction of drift-diffusion equations in parametrized electrical networks. (English) Zbl 1237.78038 ZAMM, Z. Angew. Math. Mech. 92, No. 2, 91-104 (2012). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 78M10 82D37 65L60 37N20 78M34 PDF BibTeX XML Cite \textit{M. Hinze} and \textit{M. Kunkel}, ZAMM, Z. Angew. Math. Mech. 92, No. 2, 91--104 (2012; Zbl 1237.78038) Full Text: DOI arXiv OpenURL
Wu, Bin Existence of weak solutions to a degenerate stead-state semiconductor equation. (English) Zbl 1240.35551 Acta Math. Sci., Ser. B, Engl. Ed. 31, No. 3, 960-968 (2011). MSC: 35Q82 35A01 35D30 35M33 82D37 PDF BibTeX XML Cite \textit{B. Wu}, Acta Math. Sci., Ser. B, Engl. Ed. 31, No. 3, 960--968 (2011; Zbl 1240.35551) Full Text: DOI OpenURL
Yamamoto, Masakazu Spatial analyticity of solutions to the drift-diffusion equation with generalized dissipation. (English) Zbl 1225.35042 Arch. Math. 97, No. 3, 261-270 (2011). MSC: 35B65 35K45 35Q60 78A35 82D37 35R11 PDF BibTeX XML Cite \textit{M. Yamamoto}, Arch. Math. 97, No. 3, 261--270 (2011; Zbl 1225.35042) Full Text: DOI OpenURL
Yamamoto, Masakazu Asymptotic expansion of solution to the Nernst-Planck drift-diffusion equation. (English) Zbl 1203.35043 RIMS Kôkyûroku Bessatsu B15, 189-208 (2009). Reviewer: Il’ya Sh. Mogilevskij (Tver’) MSC: 35B40 35K45 35K55 82D37 35Q60 PDF BibTeX XML Cite \textit{M. Yamamoto}, RIMS Kôkyûroku Bessatsu B15, 189--208 (2009; Zbl 1203.35043) OpenURL
Mickens, Ronald E. A nonstandard finite difference scheme for the drift-diffusion system. (English) Zbl 1187.82137 Discrete Contin. Dyn. Syst. 2009, Suppl., 558-563 (2009). MSC: 82D37 65M06 78A60 PDF BibTeX XML Cite \textit{R. E. Mickens}, Discrete Contin. Dyn. Syst. 2009, 558--563 (2009; Zbl 1187.82137) OpenURL
Cole, E. A. B. Mathematical and numerical modelling of heterostructure semiconductor devices: From theory to programming. (English) Zbl 1252.82004 London: Springer (ISBN 978-1-84882-936-7/pbk; 978-1-84882-937-4/ebook). xv, 406 p. (2009). Reviewer: Georg Hebermehl (Berlin) MSC: 82-02 81-02 82D37 82C70 82-08 82B80 65M06 65N06 65H10 65F05 65F10 65F15 65K10 65D30 35Q55 35Q41 35Q61 94C05 78A25 78A55 PDF BibTeX XML Cite \textit{E. A. B. Cole}, Mathematical and numerical modelling of heterostructure semiconductor devices: From theory to programming. London: Springer (2009; Zbl 1252.82004) Full Text: DOI OpenURL
Lin, Paul T.; Shadid, John N.; Sala, Marzio; Tuminaro, Raymond S.; Hennigan, Gary L.; Hoekstra, Robert J. Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling. (English) Zbl 1175.82077 J. Comput. Phys. 228, No. 17, 6250-6267 (2009). MSC: 82D37 65M60 65F10 65F08 78A35 PDF BibTeX XML Cite \textit{P. T. Lin} et al., J. Comput. Phys. 228, No. 17, 6250--6267 (2009; Zbl 1175.82077) Full Text: DOI OpenURL
Xu, Jiang Relaxation-time limit in the isothermal hydrodynamic model for semiconductors. (English) Zbl 1181.35015 SIAM J. Math. Anal. 40, No. 5, 1979-1991 (2009). MSC: 35B25 35L45 82D37 PDF BibTeX XML Cite \textit{J. Xu}, SIAM J. Math. Anal. 40, No. 5, 1979--1991 (2009; Zbl 1181.35015) Full Text: DOI OpenURL
Burger, Martin; Pinnau, René A globally convergent Gummel map for optimal dopant profiling. (English) Zbl 1173.35706 Math. Models Methods Appl. Sci. 19, No. 5, 769-786 (2009). MSC: 35Q60 35J50 49J20 49K20 78M50 35Q55 82D37 PDF BibTeX XML Cite \textit{M. Burger} and \textit{R. Pinnau}, Math. Models Methods Appl. Sci. 19, No. 5, 769--786 (2009; Zbl 1173.35706) Full Text: DOI OpenURL
Seoane, Natalia; García-Loureiro, Antonio; Aldegunde, Manuel Optimization of linear systems for 3D parallel simulation of semiconductor devices: Application to statistical studies. (English) Zbl 1162.82027 Int. J. Numer. Model. 22, No. 3, 235-258 (2009). MSC: 82D37 35J05 65Y05 65F05 65N55 65F10 PDF BibTeX XML Cite \textit{N. Seoane} et al., Int. J. Numer. Model. 22, No. 3, 235--258 (2009; Zbl 1162.82027) Full Text: DOI OpenURL
de Falco, Carlo; Jerome, Joseph W.; Sacco, Riccardo Quantum-corrected drift-diffusion models: Solution fixed point map and finite element approximation. (English) Zbl 1158.82012 J. Comput. Phys. 228, No. 5, 1770-1789 (2009). MSC: 82D37 65N30 PDF BibTeX XML Cite \textit{C. de Falco} et al., J. Comput. Phys. 228, No. 5, 1770--1789 (2009; Zbl 1158.82012) Full Text: DOI OpenURL
Escobedo, Ramón; Bonilla, Luis L. Numerical methods for a quantum drift-diffusion equation in semiconductor physics. (English) Zbl 1104.82051 J. Math. Chem. 40, No. 1, 3-13 (2006). MSC: 82D37 37M05 37N20 81T80 65M06 82C70 PDF BibTeX XML Cite \textit{R. Escobedo} and \textit{L. L. Bonilla}, J. Math. Chem. 40, No. 1, 3--13 (2006; Zbl 1104.82051) Full Text: DOI OpenURL
Giraud, L.; Marrocco, A.; Rioual, J.-C. Iterative versus direct parallel substructuring methods in semiconductor device modelling. (English) Zbl 1164.82327 Numer. Linear Algebra Appl. 12, No. 1, 33-53 (2005). Reviewer: Jan Chleboun (Praha) MSC: 82D37 65N55 65Y05 65F10 65F05 PDF BibTeX XML Cite \textit{L. Giraud} et al., Numer. Linear Algebra Appl. 12, No. 1, 33--53 (2005; Zbl 1164.82327) Full Text: DOI OpenURL
El Boukili, A.; Madrane, A.; Vaillantcourt, R. Multifrontal solution of sparse unsymmetric matrices arising from semiconductor equations. (English) Zbl 1076.65027 Can. Appl. Math. Q. 12, No. 2, 137-152 (2004). MSC: 65F05 65F50 82D37 82-08 PDF BibTeX XML Cite \textit{A. El Boukili} et al., Can. Appl. Math. Q. 12, No. 2, 137--152 (2004; Zbl 1076.65027) OpenURL
Chainais-Hillairet, Claire; Peng, Yue-Jun Finite volume approximation for degenerate drift-diffusion system in several space dimensions. (English) Zbl 1127.65319 Math. Models Methods Appl. Sci. 14, No. 3, 461-481 (2004). MSC: 65M06 65M12 35M10 35K45 35J70 82D37 PDF BibTeX XML Cite \textit{C. Chainais-Hillairet} and \textit{Y.-J. Peng}, Math. Models Methods Appl. Sci. 14, No. 3, 461--481 (2004; Zbl 1127.65319) Full Text: DOI OpenURL
Guo, Xiulan; Li, Kaitai Asymptotic behavior of the drift-diffusion semiconductor equations. (English) Zbl 1072.35177 Acta Math. Sci., Ser. B, Engl. Ed. 24, No. 3, 385-394 (2004). Reviewer: Joachim Naumann (Berlin) MSC: 35Q60 82D37 37L30 35B41 PDF BibTeX XML Cite \textit{X. Guo} and \textit{K. Li}, Acta Math. Sci., Ser. B, Engl. Ed. 24, No. 3, 385--394 (2004; Zbl 1072.35177) Full Text: DOI OpenURL
Micheletti, Stefano; Sacco, Riccardo; Simioni, Paolo Numerical simulation of resonant tunneling diodes with a quantum-drift-diffusion model. (English) Zbl 1074.82030 Schilders, Wilhelmus H. A. (ed.) et al., Scientific computing in electrical engineering. Proceedings of the SCEE 2002 Conference, Eindhoven, The Netherlands, June 23–28, 2002. Berlin: Springer (ISBN 3-540-21372-4/hbk). Mathematics in Industry 4. The European Consortium for Mathematics in Industry, 313-320 (2004). Reviewer: Guy Jumarie (Montréal) MSC: 82D37 65N30 65H10 PDF BibTeX XML Cite \textit{S. Micheletti} et al., Math. Ind. 4, 313--320 (2004; Zbl 1074.82030) OpenURL
Yong, Wen-An Diffusive relaxation limit of multidimensional isentropic hydrodynamical models for semiconductors. (English) Zbl 1053.35084 SIAM J. Appl. Math. 64, No. 5, 1737-1748 (2004). MSC: 35L45 35B25 35Q60 82D37 65M06 65M12 PDF BibTeX XML Cite \textit{W.-A. Yong}, SIAM J. Appl. Math. 64, No. 5, 1737--1748 (2004; Zbl 1053.35084) Full Text: DOI OpenURL
Alí, Giuseppe; Bartel, Andreas; Günther, Michael; Tischendorf, Caren Elliptic partial differential-algebraic multiphysics models in electrical network design. (English) Zbl 1046.94519 Math. Models Methods Appl. Sci. 13, No. 9, 1261-1278 (2003). MSC: 94C99 35J25 82D37 PDF BibTeX XML Cite \textit{G. Alí} et al., Math. Models Methods Appl. Sci. 13, No. 9, 1261--1278 (2003; Zbl 1046.94519) Full Text: DOI OpenURL
Burger, Martin; Pinnau, René Fast optimal design of semiconductor devices. (English) Zbl 1056.49035 SIAM J. Appl. Math. 64, No. 1, 108-126 (2003). MSC: 49N90 35J50 35J55 90C46 82D37 PDF BibTeX XML Cite \textit{M. Burger} and \textit{R. Pinnau}, SIAM J. Appl. Math. 64, No. 1, 108--126 (2003; Zbl 1056.49035) Full Text: DOI OpenURL
Hinze, Michael; Pinnau, René An optimal control approach to semiconductor design. (English) Zbl 1173.49302 Math. Models Methods Appl. Sci. 12, No. 1, 89-107 (2002). MSC: 49J20 49K20 82D37 35J15 35J50 PDF BibTeX XML Cite \textit{M. Hinze} and \textit{R. Pinnau}, Math. Models Methods Appl. Sci. 12, No. 1, 89--107 (2002; Zbl 1173.49302) Full Text: DOI OpenURL
Ringhofer, Christian An entropy-based finite difference method for the energy transport system. (English) Zbl 1012.65091 Math. Models Methods Appl. Sci. 11, No. 5, 769-795 (2001). MSC: 65M06 78A35 78M20 35Q60 82D37 82C70 PDF BibTeX XML Cite \textit{C. Ringhofer}, Math. Models Methods Appl. Sci. 11, No. 5, 769--795 (2001; Zbl 1012.65091) Full Text: DOI OpenURL
Xing, Jiasheng Asymptotic behavior of the drift-diffusion semiconductor equations. (Chinese. English summary) Zbl 0974.35121 J. Zhengzhou Univ., Nat. Sci. Ed. 32, No. 3, 1-6 (2000). MSC: 35Q60 82D37 37L30 PDF BibTeX XML Cite \textit{J. Xing}, J. Zhengzhou Univ., Nat. Sci. Ed. 32, No. 3, 1--6 (2000; Zbl 0974.35121) OpenURL
Belyavskij, S. S.; Mulyarchik, S. G. Approximate solution to the transfer equation. (Russian. English summary) Zbl 0955.65075 Tr. Inst. Mat., Minsk 6, 27-30 (2000). Reviewer: Sergei V.Rogosin (Minsk) MSC: 65N06 82D37 35J25 PDF BibTeX XML Cite \textit{S. S. Belyavskij} and \textit{S. G. Mulyarchik}, Tr. Inst. Mat., Minsk 6, 27--30 (2000; Zbl 0955.65075) OpenURL
Allegretto, W.; Lin, Y.; Zhou, A. Numerical analysis for systems with memory arising from semiconductor simulations. (English) Zbl 1022.65115 Appl. Math. Comput. 105, No. 2-3, 101-119 (1999). MSC: 65M60 65M20 65M15 65M12 35K45 82D37 PDF BibTeX XML Cite \textit{W. Allegretto} et al., Appl. Math. Comput. 105, No. 2--3, 101--119 (1999; Zbl 1022.65115) Full Text: DOI OpenURL
Romano, Vittorio; Torrisi, Mariano Application of weak equivalence transformations to a group analysis of a drift-diffusion model. (English) Zbl 0947.35009 J. Phys. A, Math. Gen. 32, No. 45, 7953-7963 (1999). Reviewer: Samir Musayev (Baku) MSC: 35A22 58J70 35A30 PDF BibTeX XML Cite \textit{V. Romano} and \textit{M. Torrisi}, J. Phys. A, Math. Gen. 32, No. 45, 7953--7963 (1999; Zbl 0947.35009) Full Text: DOI Link OpenURL
Schenk, Olaf; Gärtner, Klaus; Schmithüsen, Bernhard; Fichtner, Wolfgang Numerical semiconductor device and process simulation on shared memory multiprocessors: Algorithms, architectures, results. (English) Zbl 0946.65017 Yang, Tianruo (ed.), Parallel numerical computation with applications. Proceedings of the workshop on Frontiers of parallel numerical computations and applications, organized in the IEEE 7th symposium on the Frontiers on massively parallel computers (Frontiers ’99) at Annapolis, MD, USA, February 20-25, 1999. Boston: Kluwer Academic Publishers. Kluwer Int. Ser. Eng. Comput. Sci. 515, 141-157 (1999). MSC: 65F05 35Q60 65Y05 65Y15 82D37 PDF BibTeX XML Cite \textit{O. Schenk} et al., Kluwer Int. Ser. Eng. Comput. Sci. 515, 141--157 (1999; Zbl 0946.65017) OpenURL