메뉴 건너뛰기




Volumn 228, Issue 17, 2009, Pages 6250-6267

Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling

Author keywords

Drift diffusion; Finite element; Graph partitioning; Multigrid; Multilevel preconditioners; Newton Krylov; Nonsmoothed aggregation; Schwarz domain decomposition; Semiconductor devices

Indexed keywords

DIFFUSION; DOMAIN DECOMPOSITION METHODS; ELECTRIC POTENTIAL; FINITE ELEMENT METHOD; GRAPH THEORY; HOLE CONCENTRATION; NUMERICAL METHODS; POISSON EQUATION; SCALABILITY; SEMICONDUCTOR DEVICE MODELS; SEMICONDUCTOR DEVICES;

EID: 67650355495     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.05.024     Document Type: Article
Times cited : (48)

References (54)
  • 3
    • 84916389355 scopus 로고
    • Large-signal analysis of a silicon read diode oscillator
    • Scharfetter D.L., and Gummel H.K. Large-signal analysis of a silicon read diode oscillator. IEEE Trans. Electron Dev. 16 1 (1969) 64-77
    • (1969) IEEE Trans. Electron Dev. , vol.16 , Issue.1 , pp. 64-77
    • Scharfetter, D.L.1    Gummel, H.K.2
  • 4
    • 84916430884 scopus 로고
    • A self-consistent iterative scheme for one-dimensional steady state transistor calculations
    • Gummel H.K. A self-consistent iterative scheme for one-dimensional steady state transistor calculations. IEEE Trans. Electron Dev. ED-11 (1964) 455-465
    • (1964) IEEE Trans. Electron Dev. , vol.ED-11 , pp. 455-465
    • Gummel, H.K.1
  • 5
    • 85190568140 scopus 로고    scopus 로고
    • Medici two-dimensional device simulation program user manual, Technical Report, Synopsys, February 2003.
    • Medici two-dimensional device simulation program user manual, Technical Report, Synopsys, February 2003.
  • 6
    • 85190569504 scopus 로고    scopus 로고
    • Davinci three-dimensional device simulation program manual type, Technical Report, Synopsys, February 2003.
    • Davinci three-dimensional device simulation program manual type, Technical Report, Synopsys, February 2003.
  • 7
    • 0001677033 scopus 로고    scopus 로고
    • A multigrid preconditioner for the semiconductor equations
    • Meza J.C., and Tuminaro R.S. A multigrid preconditioner for the semiconductor equations. SIAM J. Sci. Comput. 17 1 (1996) 118-132
    • (1996) SIAM J. Sci. Comput. , vol.17 , Issue.1 , pp. 118-132
    • Meza, J.C.1    Tuminaro, R.S.2
  • 9
    • 11544342551 scopus 로고
    • A multigrid approach for the solution of the 2D semiconductor equations
    • Molenaar J., and Hemker P.W. A multigrid approach for the solution of the 2D semiconductor equations. Impact Comput. Sci. Eng. 2 (1990) 219-243
    • (1990) Impact Comput. Sci. Eng. , vol.2 , pp. 219-243
    • Molenaar, J.1    Hemker, P.W.2
  • 10
    • 0348198275 scopus 로고    scopus 로고
    • Jacobian-free Newton-Krylov methods: a survey of approaches and applications
    • Knoll D.A., and Keyes D.E. Jacobian-free Newton-Krylov methods: a survey of approaches and applications. J. Comput. Phys. 193 (2004) 357-397
    • (2004) J. Comput. Phys. , vol.193 , pp. 357-397
    • Knoll, D.A.1    Keyes, D.E.2
  • 11
    • 33745925596 scopus 로고    scopus 로고
    • Performance of fully-coupled algebraic multilevel domain decomposition preconditioners for incompressible flow and transport
    • Lin P.T., Sala M., Shadid J.N., and Tuminaro R.S. Performance of fully-coupled algebraic multilevel domain decomposition preconditioners for incompressible flow and transport. Int. J. Numer. Meth. Eng. 67 2 (2006) 208-225
    • (2006) Int. J. Numer. Meth. Eng. , vol.67 , Issue.2 , pp. 208-225
    • Lin, P.T.1    Sala, M.2    Shadid, J.N.3    Tuminaro, R.S.4
  • 12
    • 33746134787 scopus 로고    scopus 로고
    • An improved convergence bound for aggregation-based domain decomposition preconditioners
    • Sala M., Shadid J.N., and Tuminaro R.S. An improved convergence bound for aggregation-based domain decomposition preconditioners. SIAM J. Matrix Anal. 27 3 (2006) 744-756
    • (2006) SIAM J. Matrix Anal. , vol.27 , Issue.3 , pp. 744-756
    • Sala, M.1    Shadid, J.N.2    Tuminaro, R.S.3
  • 13
    • 16844376040 scopus 로고    scopus 로고
    • Performance of fully-coupled domain decomposition preconditioners for finite element transport/reaction simulations
    • Shadid J.N., Tuminaro R.S., Devine K.D., Hennigan G.L., and Lin P.T. Performance of fully-coupled domain decomposition preconditioners for finite element transport/reaction simulations. J. Comput. Phys. 205 1 (2005) 24-47
    • (2005) J. Comput. Phys. , vol.205 , Issue.1 , pp. 24-47
    • Shadid, J.N.1    Tuminaro, R.S.2    Devine, K.D.3    Hennigan, G.L.4    Lin, P.T.5
  • 15
    • 0030388574 scopus 로고    scopus 로고
    • Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
    • Vaněk P., Mandel J., and Brezina M. Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing 56 (1996) 179-196
    • (1996) Computing , vol.56 , pp. 179-196
    • Vaněk, P.1    Mandel, J.2    Brezina, M.3
  • 16
    • 0041034172 scopus 로고    scopus 로고
    • Convergence of algebraic multigrid based on smoothed aggregation
    • Vaněk P., Brezina M., and Mandel J. Convergence of algebraic multigrid based on smoothed aggregation. Numer. Math. 88 (2001) 559-579
    • (2001) Numer. Math. , vol.88 , pp. 559-579
    • Vaněk, P.1    Brezina, M.2    Mandel, J.3
  • 17
    • 0003561904 scopus 로고
    • Multilevel k-way partitioning scheme for irregular graphs
    • Technical Report 95-064, Department of Computer Science, University of Minnesota
    • G. Karypis, V. Kumar, Multilevel k-way partitioning scheme for irregular graphs, Technical Report 95-064, Department of Computer Science, University of Minnesota, 1995.
    • (1995)
    • Karypis, G.1    Kumar, V.2
  • 18
    • 0003798972 scopus 로고    scopus 로고
    • ParMETIS: Parallel graph partitioning and sparse matrix ordering library
    • Technical Report 97-060, Department of Computer Science, University of Minnesota
    • G. Karypis, V. Kumar, ParMETIS: parallel graph partitioning and sparse matrix ordering library, Technical Report 97-060, Department of Computer Science, University of Minnesota, 1997.
    • (1997)
    • Karypis, G.1    Kumar, V.2
  • 19
    • 0039064853 scopus 로고
    • Nonlinear multigrid applied to a one-dimensional stationary semiconductor model
    • De Zeeuw P.M. Nonlinear multigrid applied to a one-dimensional stationary semiconductor model. SIAM J. Sci. Stat. Comput. 13 2 (1992) 512-530
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , Issue.2 , pp. 512-530
    • De Zeeuw, P.M.1
  • 20
    • 67650504003 scopus 로고
    • Continuation and multi-grid for nonlinear elliptic systems
    • W. Hackbusch, U. Trottenberg Eds, Multigrid Methods II Proceedings of the 2nd European Conference on Multigrid Methods, Springer-Verlag
    • R.E. Bank, H.D. Mittelmann, Continuation and multi-grid for nonlinear elliptic systems, in: W. Hackbusch, U. Trottenberg (Eds.), Multigrid Methods II Proceedings of the 2nd European Conference on Multigrid Methods, Lecture Notes in Mathematics, vol. 2, Springer-Verlag, 1986, pp. 23-37.
    • (1986) Lecture Notes in Mathematics , vol.2 , pp. 23-37
    • Bank, R.E.1    Mittelmann, H.D.2
  • 21
    • 0020259662 scopus 로고
    • A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions: application to the streamline-upwind procedure
    • Gallagher R.H., et al. (Ed), J. Willey & Sons pp. 47-65
    • Hughes T.J.R., and Brooks A. A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions: application to the streamline-upwind procedure. In: Gallagher R.H., et al. (Ed). Finite Elements in Fluids vol. 4 (1982), J. Willey & Sons pp. 47-65
    • (1982) Finite Elements in Fluids , vol.4
    • Hughes, T.J.R.1    Brooks, A.2
  • 22
    • 0022681271 scopus 로고
    • A new finite element formulation for computational fluid dynamics: II. Beyond SUPG
    • Hughes T.J.R., Mallet M., and Mizukami A. A new finite element formulation for computational fluid dynamics: II. Beyond SUPG. Comput. Meth. Appl. Mech. Eng. 54 (1986) 341-355
    • (1986) Comput. Meth. Appl. Mech. Eng. , vol.54 , pp. 341-355
    • Hughes, T.J.R.1    Mallet, M.2    Mizukami, A.3
  • 24
    • 0024681303 scopus 로고
    • Semiconductor device simulation using adaptive refinement and flux upwinding
    • Sharma M., and Carey G.F. Semiconductor device simulation using adaptive refinement and flux upwinding. IEEE Trans. Computer-Aided Des. 8 6 (1989) 590-598
    • (1989) IEEE Trans. Computer-Aided Des. , vol.8 , Issue.6 , pp. 590-598
    • Sharma, M.1    Carey, G.F.2
  • 25
    • 85190570802 scopus 로고    scopus 로고
    • Advanced numerical methods and software approaches for semiconductor device simulation
    • Technical Report SAND2000-0763J, Sandia National Laboratories
    • G.F. Carey, A.L. Pardhanani, S.W. Bova, Advanced numerical methods and software approaches for semiconductor device simulation, Technical Report SAND2000-0763J, Sandia National Laboratories, 2000.
    • (2000)
    • Carey, G.F.1    Pardhanani, A.L.2    Bova, S.W.3
  • 26
    • 0000199487 scopus 로고    scopus 로고
    • Comparison of some finite element methods for solving the diffusion-convection-reaction equations
    • Codina R. Comparison of some finite element methods for solving the diffusion-convection-reaction equations. Comput. Meth. Appl. Mech. Eng. 156 (1998) 185-210
    • (1998) Comput. Meth. Appl. Mech. Eng. , vol.156 , pp. 185-210
    • Codina, R.1
  • 28
    • 85190568670 scopus 로고    scopus 로고
    • Performance of stabilized finite element methods for solution of the drift-diffusion equations of semiconductor modeling
    • in preparation
    • J.N. Shadid, G.L. Hennigan, P.T. Lin, R.J. Hoekstra, Performance of stabilized finite element methods for solution of the drift-diffusion equations of semiconductor modeling, in preparation.
    • Shadid, J.N.1    Hennigan, G.L.2    Lin, P.T.3    Hoekstra, R.J.4
  • 29
    • 0022807116 scopus 로고
    • A new finite element formulation for computational fluid dynamics: III.The generalized streamline operator for multidimensional advective-diffusive systems
    • Hughes T.J.R., and Mallet M. A new finite element formulation for computational fluid dynamics: III.The generalized streamline operator for multidimensional advective-diffusive systems. Comput. Meth. Appl. Mech. Eng. 58 (1986) 305-328
    • (1986) Comput. Meth. Appl. Mech. Eng. , vol.58 , pp. 305-328
    • Hughes, T.J.R.1    Mallet, M.2
  • 30
    • 0000977352 scopus 로고
    • Hybrid Krylov methods for nonlinear systems of equations
    • Brown P.N., and Saad Y. Hybrid Krylov methods for nonlinear systems of equations. SIAM J. Sci. Stat. Comput. 11 3 (1990) 450-481
    • (1990) SIAM J. Sci. Stat. Comput. , vol.11 , Issue.3 , pp. 450-481
    • Brown, P.N.1    Saad, Y.2
  • 31
    • 0033267340 scopus 로고    scopus 로고
    • A fully-coupled Newton-Krylov solution method for parallel unstructured finite element fluid flow, heat and mass transfer simulations
    • Shadid J.N. A fully-coupled Newton-Krylov solution method for parallel unstructured finite element fluid flow, heat and mass transfer simulations. Int. J. CFD 12 (1999) 199-211
    • (1999) Int. J. CFD , vol.12 , pp. 199-211
    • Shadid, J.N.1
  • 34
    • 0001330894 scopus 로고
    • Globally convergent inexact Newton methods
    • Eisenstat S.C., and Walker H.F. Globally convergent inexact Newton methods. SIAM J. Optim. 4 (1994) 393-422
    • (1994) SIAM J. Optim. , vol.4 , pp. 393-422
    • Eisenstat, S.C.1    Walker, H.F.2
  • 37
    • 0033295858 scopus 로고    scopus 로고
    • A restricted additive Schwarz preconditioner for general sparse linear systems
    • Cai X.-C., and Sarkis M. A restricted additive Schwarz preconditioner for general sparse linear systems. SIAM J. Sci. Comput. 21 (1999) 792-797
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 792-797
    • Cai, X.-C.1    Sarkis, M.2
  • 38
    • 0003603271 scopus 로고    scopus 로고
    • Aztec user's guide - version 2.1
    • Technical Report SAND99-8801J, Sandia National Laboratories, Albuquerque NM, 87185, Nov
    • R.S. Tuminaro, M. Heroux, S.A. Hutchinson, J.N. Shadid, Aztec user's guide - version 2.1, Technical Report SAND99-8801J, Sandia National Laboratories, Albuquerque NM, 87185, Nov. 1999.
    • (1999)
    • Tuminaro, R.S.1    Heroux, M.2    Hutchinson, S.A.3    Shadid, J.N.4
  • 39
    • 0002059273 scopus 로고
    • Towards a unified theory of domain decomposition algorithms for elliptic problems
    • T.F. Chan, R. Glowinski, J.Périaux, O. Widlund Eds, SIAM, Philadelphia, PA
    • M. Dryja, O.B. Widlund, Towards a unified theory of domain decomposition algorithms for elliptic problems, in: T.F. Chan, R. Glowinski, J.Périaux, O. Widlund (Eds.), Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1990, pp. 3-21.
    • (1990) Third International Symposium on Domain Decomposition Methods for Partial Differential Equations , pp. 3-21
    • Dryja, M.1    Widlund, O.B.2
  • 40
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction: a unifying approach
    • Xu J. Iterative methods by space decomposition and subspace correction: a unifying approach. SIAM Rev. 34 4 (1992) 581-613
    • (1992) SIAM Rev. , vol.34 , Issue.4 , pp. 581-613
    • Xu, J.1
  • 41
    • 0000555209 scopus 로고
    • Black box multigrid for nonsymmetric problems
    • Dendy J. Black box multigrid for nonsymmetric problems. Appl. Math. Comput. 13 (1983) 261-283
    • (1983) Appl. Math. Comput. , vol.13 , pp. 261-283
    • Dendy, J.1
  • 42
    • 55049118140 scopus 로고    scopus 로고
    • A new Petrov-Galerkin smoothed aggregation preconditioner for nonsymmetric linear systems
    • Sala M., and Tuminaro R.S. A new Petrov-Galerkin smoothed aggregation preconditioner for nonsymmetric linear systems. SIAM J. Sci. Stat. 31 (2008) 143-166
    • (2008) SIAM J. Sci. Stat. , vol.31 , pp. 143-166
    • Sala, M.1    Tuminaro, R.S.2
  • 43
    • 2942526684 scopus 로고    scopus 로고
    • Parallel smoothed aggregation multigrid: Aggregation strategies on massively parallel machines
    • J. Donnelley Ed
    • R. Tuminaro, C. Tong, Parallel smoothed aggregation multigrid: aggregation strategies on massively parallel machines, in: J. Donnelley (Ed.), SuperComputing 2000 Proceedings, 2000.
    • (2000) SuperComputing 2000 Proceedings
    • Tuminaro, R.1    Tong, C.2
  • 44
    • 0037233450 scopus 로고    scopus 로고
    • A multigrid method based on graph matching for convection-diffusion equations
    • Kim H.H., Xu J.C., and Zikatanov L. A multigrid method based on graph matching for convection-diffusion equations. Numer. Linear Algebra Appl. 10 1-2 (2003) 181-195
    • (2003) Numer. Linear Algebra Appl. , vol.10 , Issue.1-2 , pp. 181-195
    • Kim, H.H.1    Xu, J.C.2    Zikatanov, L.3
  • 47
    • 0003573801 scopus 로고
    • The Chaco user's guide-version 1.0
    • Technical Report SAND93-2339, Sandia National Laboratories, Albuquerque NM, 87185
    • B. Hendrickson, R. Leland, The Chaco user's guide-version 1.0, Technical Report SAND93-2339, Sandia National Laboratories, Albuquerque NM, 87185, 1993.
    • (1993)
    • Hendrickson, B.1    Leland, R.2
  • 51
    • 34548380842 scopus 로고    scopus 로고
    • ML 5.0 smoothed aggregation user's guide
    • Technical Report SAND2006-2649, Sandia National Laboratories
    • M.W. Gee, C.M. Siefert, J.J. Hu, R.S. Tuminaro, M.G. Sala, ML 5.0 smoothed aggregation user's guide, Technical Report SAND2006-2649, Sandia National Laboratories, 2006.
    • (2006)
    • Gee, M.W.1    Siefert, C.M.2    Hu, J.J.3    Tuminaro, R.S.4    Sala, M.G.5
  • 54
    • 0000709349 scopus 로고
    • Solution of the nonlinear Poisson equation of semiconductor device theory
    • Mayergoyz I.D. Solution of the nonlinear Poisson equation of semiconductor device theory. J. Appl. Phys 59 1 (1986) 195-199
    • (1986) J. Appl. Phys , vol.59 , Issue.1 , pp. 195-199
    • Mayergoyz, I.D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.