메뉴 건너뛰기




Volumn 161, Issue 1, 2000, Pages 312-330

Discretization of the Multiscale Semiconductor Boltzmann Equation by Diffusive Relaxation Schemes

Author keywords

Diffusive relaxation schemes; Drift diffusion limit; Semiconductor Boltzmann equation; Wild sums

Indexed keywords

BOLTZMANN EQUATION; INTEGRAL EQUATIONS;

EID: 0010663847     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6506     Document Type: Article
Times cited : (55)

References (34)
  • 1
    • 11644314632 scopus 로고
    • Even-parity finite-element transport methods in the diffusion limit
    • Adams M. L. Even-parity finite-element transport methods in the diffusion limit. Progr. Nucl. Energy. 25:1991;159.
    • (1991) Progr. Nucl. Energy , vol.25 , pp. 159
    • Adams, M.L.1
  • 2
    • 0032315415 scopus 로고    scopus 로고
    • Hyperbolic hydrodynamical model of carroer transport in semiconductors
    • Anile A. M., Romano V., Russo G. Hyperbolic hydrodynamical model of carroer transport in semiconductors. VLSI Design. 8:1998;521.
    • (1998) VLSI Design , vol.8 , pp. 521
    • Anile, A.M.1    Romano, V.2    Russo, G.3
  • 3
    • 0010115469 scopus 로고
    • The asymptotic diffusion limit of a linear discontinuous discretization of a two-dimensional linear transport equation
    • Borgers C., Larsen E. W., Adams M. L. The asymptotic diffusion limit of a linear discontinuous discretization of a two-dimensional linear transport equation. J. Comput. Phys. 98:1992;285.
    • (1992) J. Comput. Phys. , vol.98 , pp. 285
    • Borgers, C.1    Larsen, E.W.2    Adams, M.L.3
  • 4
    • 0001407297 scopus 로고    scopus 로고
    • Uniformly accurate schemes for hyperbolic systems with relaxations
    • Caflisch R., Jin S., Russo G. Uniformly accurate schemes for hyperbolic systems with relaxations. SIAM J. Numer. Anal. 34:1997;246.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 246
    • Caflisch, R.1    Jin, S.2    Russo, G.3
  • 6
    • 84980134667 scopus 로고
    • Numerical solution of Boltzmann's equation
    • Chorin A. J. Numerical solution of Boltzmann's equation. Comm. Pure Appl. Math. 25:1972;171.
    • (1972) Comm. Pure Appl. Math. , vol.25 , pp. 171
    • Chorin, A.J.1
  • 7
    • 0010490131 scopus 로고
    • Particle simulations of the semiconductor Boltzmann equation for one dimsnional inhomogeneous structures
    • Degond P., Guyot-Delaurens F. Particle simulations of the semiconductor Boltzmann equation for one dimsnional inhomogeneous structures. J. Comput. Phys. 90:1990;65.
    • (1990) J. Comput. Phys. , vol.90 , pp. 65
    • Degond, P.1    Guyot-Delaurens, F.2
  • 8
    • 0026107291 scopus 로고
    • Solution of the hydrodynamic device model using high order non oscillatory shock capturing algorithm
    • Fatemi E., Jerome J. W., Osher S. Solution of the hydrodynamic device model using high order non oscillatory shock capturing algorithm. IEEE Trans. Comput. Aided Des. 10:1991;232.
    • (1991) IEEE Trans. Comput. Aided Des. , vol.10 , pp. 232
    • Fatemi, E.1    Jerome, J.W.2    Osher, S.3
  • 10
    • 0000804338 scopus 로고    scopus 로고
    • The convergence of numerical transfer schemes in diffusive regimes. I. The discrete-ordinate method
    • Golse F., Jin S., Levermore C. D. The convergence of numerical transfer schemes in diffusive regimes. I. The discrete-ordinate method. SIAM J. Numer. Anal. 36:1999;1333.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 1333
    • Golse, F.1    Jin, S.2    Levermore, C.D.3
  • 11
    • 0033295423 scopus 로고    scopus 로고
    • Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations
    • Jin S. Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations. SIAM J. Sci. Comput. 21:1999;441.
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 441
    • Jin, S.1
  • 13
    • 0000397910 scopus 로고
    • Fully discrete numerical transfer in diffusive regimes
    • Jin S., Levermore C. D. Fully discrete numerical transfer in diffusive regimes. Transport Theory Statist. Phys. 22:1993;739.
    • (1993) Transport Theory Statist. Phys. , vol.22 , pp. 739
    • Jin, S.1    Levermore, C.D.2
  • 14
    • 0000459561 scopus 로고    scopus 로고
    • Diffusive relaxation schemes for multiscale discrete-velocity kinetic equations
    • Jin S., Pareschi L., Toscani G. Diffusive relaxation schemes for multiscale discrete-velocity kinetic equations. SIAM J. Numer. Anal. 35:1998;2405.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 2405
    • Jin, S.1    Pareschi, L.2    Toscani, G.3
  • 15
    • 85190113559 scopus 로고    scopus 로고
    • Uniformly accurate diffusive relaxation schemes for multiscale transport equations
    • in press
    • S. Jin, L. Pareschi, and, G. Toscani, Uniformly accurate diffusive relaxation schemes for multiscale transport equations, SIAM J. Numer. Anal, in press.
    • SIAM J. Numer. Anal
    • Jin, S.1    Pareschi, L.2    Toscani, G.3
  • 16
    • 84990701264 scopus 로고
    • The relaxation schemes for systems of conservation laws in arbitrary space dimensions
    • Jin S., Xin Z. The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Comm. Pure Appl. Math. 48:1995;235.
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 235
    • Jin, S.1    Xin, Z.2
  • 17
    • 0000557853 scopus 로고    scopus 로고
    • An asymptotic-induced scheme for nonstationary transport equations in the diffusive limit
    • Klar A. An asymptotic-induced scheme for nonstationary transport equations in the diffusive limit. SIAM J. Numer. Anal. 15:1998;1073.
    • (1998) SIAM J. Numer. Anal. , vol.15 , pp. 1073
    • Klar, A.1
  • 18
    • 0032205976 scopus 로고    scopus 로고
    • A numerical method for kinetic semiconductor equations in the drift diffusion limit
    • Klar A. A numerical method for kinetic semiconductor equations in the drift diffusion limit. SIAM J. Sci. Comp. 19:1998;2032.
    • (1998) SIAM J. Sci. Comp. , vol.19 , pp. 2032
    • Klar, A.1
  • 19
    • 0026997894 scopus 로고
    • The asymptotic diffusion limit of discretized transport problems
    • Larsen E. W. The asymptotic diffusion limit of discretized transport problems. Nucl. Sci. Eng. 112:1992;336.
    • (1992) Nucl. Sci. Eng. , vol.112 , pp. 336
    • Larsen, E.W.1
  • 20
    • 0001729690 scopus 로고
    • Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II
    • Larsen E. W., Morel J. E. Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II. J. Comput. Phys. 83:1989;212.
    • (1989) J. Comput. Phys. , vol.83 , pp. 212
    • Larsen, E.W.1    Morel, J.E.2
  • 21
    • 0000718834 scopus 로고
    • Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes
    • Larsen E. W., Morel J. E., Miller W. F. Jr. Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes. J. Comput. Phys. 69:1987;283.
    • (1987) J. Comput. Phys. , vol.69 , pp. 283
    • Larsen, E.W.1    Morel, J.E.2    Miller W.F., Jr.3
  • 23
    • 21844500073 scopus 로고
    • Diffusion approximation of nonlinear electron phonon collision mechanism
    • Markowich P., Poupaud F., Schmeiser C. Diffusion approximation of nonlinear electron phonon collision mechanism. Math. Model. Numer. Anal. 29:1995;857.
    • (1995) Math. Model. Numer. Anal. , vol.29 , pp. 857
    • Markowich, P.1    Poupaud, F.2    Schmeiser, C.3
  • 26
    • 0026189205 scopus 로고
    • An Analysis of the finite-differenced, even-parity discrete-ordinate equations in slab geometry
    • Miller W. F. Jr. An Analysis of the finite-differenced, even-parity discrete-ordinate equations in slab geometry. Nucl. Sci. Eng. 108:1990;247.
    • (1990) Nucl. Sci. Eng. , vol.108 , pp. 247
    • Miller W.F., Jr.1
  • 27
    • 0010662626 scopus 로고    scopus 로고
    • Numerical schemes for kinetic equations in diffusive regimes
    • Naldi G., Pareschi L. Numerical schemes for kinetic equations in diffusive regimes. Appl. Math. Lett. 11:1998;29.
    • (1998) Appl. Math. Lett. , vol.11 , pp. 29
    • Naldi, G.1    Pareschi, L.2
  • 28
    • 85030058697 scopus 로고    scopus 로고
    • Numerical schemes for hyperbolic systems of conservation laws with stiff diffusive relaxation
    • to appear
    • G. Naldi, and, L. Pareschi, Numerical schemes for hyperbolic systems of conservation laws with stiff diffusive relaxation, SIAM J. Numer. Anal, to appear.
    • SIAM J. Numer. Anal
    • Naldi, G.1    Pareschi, L.2
  • 29
    • 0347699370 scopus 로고    scopus 로고
    • Asymptotic preserving Monte-Carlo methods for the Boltzmann equation
    • to appear
    • L. Pareschi, and, G. Russo, Asymptotic preserving Monte-Carlo methods for the Boltzmann equation, Transport Theory Statist. Phys, to appear.
    • Transport Theory Statist. Phys
    • Pareschi, L.1    Russo, G.2
  • 30
    • 84974753119 scopus 로고
    • Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers
    • Poupaud E. Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers. Asymptot. Anal. 4:1991;293.
    • (1991) Asymptot. Anal. , vol.4 , pp. 293
    • Poupaud, E.1
  • 32
    • 0002224298 scopus 로고    scopus 로고
    • Convergence of moment method for linear kinetic equations
    • Schmeiser C., Zwirchmayr A. Convergence of moment method for linear kinetic equations. SIAM J. Numer. Anal. 36:1998;74.
    • (1998) SIAM J. Numer. Anal. , vol.36 , pp. 74
    • Schmeiser, C.1    Zwirchmayr, A.2
  • 33
    • 0001961963 scopus 로고
    • Multidimensional spherical harmonics expansion of Bolztmann equation for transport in semiconductors
    • Ventura D., Gnudi A., Baccarani G., Odeh F. Multidimensional spherical harmonics expansion of Bolztmann equation for transport in semiconductors. Appl. Math. Lett. 5:1992;85.
    • (1992) Appl. Math. Lett. , vol.5 , pp. 85
    • Ventura, D.1    Gnudi, A.2    Baccarani, G.3    Odeh, F.4
  • 34
    • 84959596494 scopus 로고
    • On Boltzmann's equation in the kinetic theory of gases
    • Wild E. On Boltzmann's equation in the kinetic theory of gases. Proc. Camb. Phil. Soc. 47:1951;602.
    • (1951) Proc. Camb. Phil. Soc. , vol.47 , pp. 602
    • Wild, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.