## WENO

 swMATH ID: 12694 Software Authors: Carrillo, José A.; Gamba, Irene M.; Majorana, Armando; Shu, Chi-Wang Description: A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: Performance and comparisons with Monte Carlo methods. In this paper we develop a deterministic high order accurate finite-difference WENO solver to the solution of the 1-D Boltzmann-Poisson system for semiconductor devices. We follow the work in E. Fatemi and F. Odeh [J. Comput. Phys. 108, 209–217 (1993; Zbl 0792.65110)] and in A. Majorana and R. Pidatella [J. Comput. Phys. 174, 649–668 (2001; Zbl 0992.82047)] to formulate the Boltzmann-Poisson system in a spherical coordinate system using the energy as one of the coordinate variables, thus reducing the computational complexity to two dimensions in phase space and dramatically simplifying the evaluations of the collision terms. The solver is accurate in time hence potentially useful for time-dependent simulations, although in this paper we only test it for steady-state devices. The high order accuracy and nonoscillatory properties of the solver allow us to use very coarse meshes to get a satisfactory resolution, thus making it feasible to develop a 2-D solver (which will be five dimensional plus time when the phase space is discretized) on today’s computers. The computational results have been compared with those by a Monte Carlo simulation and excellent agreements have been found. The advantage of the current solver over a Monte Carlo solver includes its faster speed, noise-free resolution, and easiness for arbitrary moment evaluations. This solver is thus a useful benchmark to check on the physical validity of various hydrodynamic and energy transport models. Some comparisons have been included in this paper. Homepage: http://www.sciencedirect.com/science/article/pii/S0021999102000323 Keywords: Boltzmann–Poisson system; WENO scheme; High order accuracy; Semiconductor devices Related Software: Vador; HE-E1GODF; GaAs-MESFET; HLLE; KIOPS; imexLNL; ImplicitLNLMethods; phipm; Algorithm 919; Expint; Expokit; OpenMPI; LAPACK; RODAS; BARON; Boltzmann Cited in: 54 Publications
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### Cited by 77 Authors

 10 Martínez Gamba, Irene 10 Majorana, Armando 8 Carrillo de la Plata, José Antonio 8 Shu, Chi-Wang 7 Schürrer, Ferdinand 5 Cáceres, María-José 5 Cheng, Yingda 5 Galler, Martin 4 Gottlieb, Sigal 4 Vecil, Francesco 3 Auer, Christopher 3 Ketcheson, David I. 3 Mantas, José Miguel 3 Romano, Vittorio 2 Cale, Timothy S. 2 Gobbert, Matthias K. 2 Grant, Zachary J. 2 Li, Ruo 2 Lu, Tiao 2 Morales Escalante, José A. 2 Ren, Kui 2 Russo, Giovanni 1 Adami, Stefan 1 Adams, Nikolaus A. 1 Alekseenko, Alexander M. 1 Baker, Lowell L. 1 Battiato, Marco 1 Besse, Christophe 1 Bresten, Christopher 1 Chelikowsky, James R. 1 Chen, Shi 1 Chen, Yanping 1 Chen, Zheng 1 Di, Yana 1 Domaingo, A. 1 Du, Gang 1 Ertler, C. 1 Fan, Yuwei 1 Filbet, Francis 1 Fleischmann, Nico 1 Gámiz, Francisco 1 Gillman, Adrianna 1 Godoy, Andrés 1 Goudon, Thierry 1 Hadjiconstantinou, Nicolas G. 1 He, Yuan 1 Higgs, Daniel 1 Isherwood, Leah F. 1 Jin, Shi 1 Kou, Zhenzhong 1 Larosa, Salvatore 1 Lee, Heung-Chan 1 Li, Fengyan 1 Li, Qin 1 Liu, Xiaoyan 1 Liu, Yunxian 1 Macdonald, Colin B. 1 Marano, Salvatore Angelo 1 Mascali, Giovanni 1 Muljadi, Bagus Putra 1 Németh, Adrián 1 Pieraccini, Sandra 1 Proft, Jennifer 1 Puppo, Gabriella 1 Sampedro, Carlos 1 Schneider, Ricarda 1 Singh, Satyvir 1 Tharkabhushanam, Sri Harsha 1 Wang, Li 1 Wang, Yanli 1 Webster, Samuel G. 1 Yan, Bokai 1 Yang, Jaw-Yen 1 Yao, Wenqi 1 Zhang, Pingwen 1 Zhang, Yongtao 1 Zhu, Xiaozhi
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### Cited in 27 Serials

 8 Journal of Computational Physics 6 Journal of Scientific Computing 3 Computer Methods in Applied Mechanics and Engineering 3 Communications in Computational Physics 2 Transport Theory and Statistical Physics 2 Mathematics of Computation 2 SIAM Journal on Numerical Analysis 2 Applied Numerical Mathematics 2 COMPEL 2 SIAM Journal on Applied Mathematics 2 SIAM Journal on Scientific Computing 1 Computers and Fluids 1 Computers & Mathematics with Applications 1 International Journal for Numerical Methods in Fluids 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Journal of Physics A: Mathematical and General 1 SIAM Review 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Multiscale Modeling & Simulation 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 Series on Advances in Mathematics for Applied Sciences 1 S$$\vec{\text{e}}$$MA Journal 1 Research in the Mathematical Sciences 1 International Journal of Applied and Computational Mathematics
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### Cited in 13 Fields

 38 Statistical mechanics, structure of matter (82-XX) 27 Numerical analysis (65-XX) 20 Fluid mechanics (76-XX) 19 Partial differential equations (35-XX) 7 Optics, electromagnetic theory (78-XX) 2 Ordinary differential equations (34-XX) 2 Integral equations (45-XX) 2 Astronomy and astrophysics (85-XX) 2 Biology and other natural sciences (92-XX) 1 Operator theory (47-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX)