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Volumn 64, Issue 6, 2005, Pages 819-848

An adaptive hybrid time-stepping scheme for highly non-linear strongly coupled problems

Author keywords

Coupled problems; Fractional step methods; Hybrid scheme; Microlithography; Operator splitting; Silylation; Time stepping

Indexed keywords

CHEMICAL REACTIONS; COMPUTER SIMULATION; DEFORMATION; DIFFUSION; MATHEMATICAL OPERATORS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; POLYMERS; PROBLEM SOLVING;

EID: 26844554462     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1399     Document Type: Article
Times cited : (9)

References (44)
  • 2
    • 0003441443 scopus 로고
    • Oxford Applied Mathematics and Computing Science Series. Oxford University Press: Oxford
    • Wood WL. Practical Time-stepping Schemes. Oxford Applied Mathematics and Computing Science Series. Oxford University Press: Oxford, 1990.
    • (1990) Practical Time-stepping Schemes
    • Wood, W.L.1
  • 3
    • 0041439238 scopus 로고    scopus 로고
    • Numerical simulation of Case II diffusion in one dimension
    • Technical Report UCB/SEMM-2002/07, University of California, Berkeley
    • Vijalapura PK. Numerical simulation of Case II diffusion in one dimension. Technical Report UCB/SEMM-2002/07, University of California, Berkeley, 2002.
    • (2002)
    • Vijalapura, P.K.1
  • 5
    • 0035973364 scopus 로고    scopus 로고
    • Remarks on the interpretation of current non-linear finite element analysis as differential-algebraic equations
    • Ellsiepen E, Hartmann S. Remarks on the interpretation of current non-linear finite element analysis as differential-algebraic equations. International Journal for Numerical Methods in Engineering 2001; 51: 679-707.
    • (2001) International Journal for Numerical Methods in Engineering , vol.51 , pp. 679-707
    • Ellsiepen, E.1    Hartmann, S.2
  • 6
    • 2642556997 scopus 로고    scopus 로고
    • Finite element analysis of transient thermoelastic behaviors in disk brakes
    • Choi JH, Lee I. Finite element analysis of transient thermoelastic behaviors in disk brakes. Wear 2004; 1-2:47-58.
    • (2004) Wear , vol.1-2 , pp. 47-58
    • Choi, J.H.1    Lee, I.2
  • 7
    • 0345708392 scopus 로고    scopus 로고
    • Coupled chemo-mechanical deterioration of cementitious materials - Part II: Numerical methods and simulation
    • Kuhl D, Bangert F, Meschke G. Coupled chemo-mechanical deterioration of cementitious materials-part II: Numerical methods and simulation. International Journal of Solids and Structures 2004; 41:41-67.
    • (2004) International Journal of Solids and Structures , vol.41 , pp. 41-67
    • Kuhl, D.1    Bangert, F.2    Meschke, G.3
  • 8
    • 0026916661 scopus 로고
    • A new unconditionally stable fractional step method for nonlinear coupled thermomechanical problems
    • Armero F, Simo JC. A new unconditionally stable fractional step method for nonlinear coupled thermomechanical problems. International Journal for Numerical Methods in Engineering 1992; 35:737-756.
    • (1992) International Journal for Numerical Methods in Engineering , vol.35 , pp. 737-756
    • Armero, F.1    Simo, J.C.2
  • 9
    • 0033115656 scopus 로고    scopus 로고
    • Formulation and finite element implementation of a multiplicative model of coupled pore-plasticity at finite strains under fully saturated conditions
    • Armero F. Formulation and finite element implementation of a multiplicative model of coupled pore-plasticity at finite strains under fully saturated conditions. Computer Methods in Applied Mechanics and Engineering 1999; 171:205-241.
    • (1999) Computer Methods in Applied Mechanics and Engineering , vol.171 , pp. 205-241
    • Armero, F.1
  • 14
    • 3142769763 scopus 로고    scopus 로고
    • A simulation system based on mixed-hybrid finite element analysis for thermal oxidation in semiconductor technology
    • Causin P, Restelli M, Sacco R. A simulation system based on mixed-hybrid finite element analysis for thermal oxidation in semiconductor technology. Computer Methods in Applied Mechanics and Engineering 2004; 193:3687-3710.
    • (2004) Computer Methods in Applied Mechanics and Engineering , vol.193 , pp. 3687-3710
    • Causin, P.1    Restelli, M.2    Sacco, R.3
  • 16
    • 26844494282 scopus 로고    scopus 로고
    • A split operator approach to reactive transport with the forward particle tracking Eulerian Lagrangian localized adjoint method
    • Bell LSJ, Binning PJ. A split operator approach to reactive transport with the forward particle tracking Eulerian Lagrangian localized adjoint method. Advances in Water Resources 2004; 23:467-492.
    • (2004) Advances in Water Resources , vol.23 , pp. 467-492
    • Bell, L.S.J.1    Binning, P.J.2
  • 17
    • 0033571420 scopus 로고    scopus 로고
    • Analysis of operator splitting for advection-diffusion-reaction problems in air pollution modelling
    • Lanser D, Verwer JG. Analysis of operator splitting for advection-diffusion-reaction problems in air pollution modelling. Journal of Computational and Applied Mathematics 1999; 111:201-216.
    • (1999) Journal of Computational and Applied Mathematics , vol.111 , pp. 201-216
    • Lanser, D.1    Verwer, J.G.2
  • 19
    • 0004086734 scopus 로고    scopus 로고
    • Moving boundary models and methods for deep submicron resist process simulation
    • Report No. UCB/ERL M99/26. Technical Report, Electronics Research Laboratory, College of Engineering, University of California, Berkeley
    • Croffie E. Moving boundary models and methods for deep submicron resist process simulation, Report No. UCB/ERL M99/26. Technical Report, Electronics Research Laboratory, College of Engineering, University of California, Berkeley, 1999.
    • (1999)
    • Croffie, E.1
  • 21
    • 0037192305 scopus 로고    scopus 로고
    • Investigation of case II diffusion behavior. 1. Theoretical studies based on the relaxation dependent solubility model
    • Sanopoulou M, Stamatialis DF, Petropoulos JH. Investigation of case II diffusion behavior. 1. Theoretical studies based on the relaxation dependent solubility model. Macromolecules 2002; 35:1012-1020.
    • (2002) Macromolecules , vol.35 , pp. 1012-1020
    • Sanopoulou, M.1    Stamatialis, D.F.2    Petropoulos, J.H.3
  • 22
    • 0020114361 scopus 로고
    • A theory of case-II diffusion
    • Thomas NL, Windle AH. A theory of case-II diffusion. Polymer 1982; 23:529-542.
    • (1982) Polymer , vol.23 , pp. 529-542
    • Thomas, N.L.1    Windle, A.H.2
  • 24
    • 0033486427 scopus 로고    scopus 로고
    • A mechanistic model of Case II diffusion of a diluent into a glassy polymer
    • Argon AS, Cohen RE, Patel AC. A mechanistic model of Case II diffusion of a diluent into a glassy polymer. Polymer 1999; 40:6991-7012.
    • (1999) Polymer , vol.40 , pp. 6991-7012
    • Argon, A.S.1    Cohen, R.E.2    Patel, A.C.3
  • 27
    • 0348198275 scopus 로고    scopus 로고
    • Jacobian-free Newton-Krylov methods: A survey of approaches and applications
    • Knoll DA, Keyes DE. Jacobian-free Newton-Krylov methods: a survey of approaches and applications. Journal of Computational Physics 2004; 193:357-397.
    • (2004) Journal of Computational Physics , vol.193 , pp. 357-397
    • Knoll, D.A.1    Keyes, D.E.2
  • 29
    • 0037051077 scopus 로고    scopus 로고
    • An adaptive-recursive staggering strategy for simulating multifield coupled processes in micro-heterogeneous solids
    • Zohdi TI. An adaptive-recursive staggering strategy for simulating multifield coupled processes in micro-heterogeneous solids. International Journal for Numerical Methods in Engineering 2002; 53:1511-1532.
    • (2002) International Journal for Numerical Methods in Engineering , vol.53 , pp. 1511-1532
    • Zohdi, T.I.1
  • 30
    • 0442281828 scopus 로고    scopus 로고
    • Modeling and simulation of a class of coupled thermo-chemo-mechanical processes in multiphase solids
    • Zohdi TI. Modeling and simulation of a class of coupled thermo-chemo-mechanical processes in multiphase solids. Computer Methods in Applied Mechanics and Engineering 2004; 193:679-699.
    • (2004) Computer Methods in Applied Mechanics and Engineering , vol.193 , pp. 679-699
    • Zohdi, T.I.1
  • 32
    • 0001518684 scopus 로고
    • On construction and comparison of difference schemes
    • Strang G. On construction and comparison of difference schemes. SIAM Journal on Numerical Analysis 1968; 5:506-517.
    • (1968) SIAM Journal on Numerical Analysis , vol.5 , pp. 506-517
    • Strang, G.1
  • 33
    • 26844434864 scopus 로고    scopus 로고
    • University of California, Berkeley, unpublished
    • Miller K. Class Notes for MATH 228A. University of California, Berkeley, 1997, unpublished.
    • (1997) Class Notes for MATH 228A
    • Miller, K.1
  • 36
    • 11744295460 scopus 로고    scopus 로고
    • Design and application of a gradient-weighted moving finite element code 1: In one dimension
    • Carlson NN, Miller K. Design and application of a gradient-weighted moving finite element code 1: in one dimension. SIAM Journal on Scientific Computing 1998; 19:728-765.
    • (1998) SIAM Journal on Scientific Computing , vol.19 , pp. 728-765
    • Carlson, N.N.1    Miller, K.2
  • 37
    • 26844497001 scopus 로고    scopus 로고
    • Numerical simulation of solvent diffusion and reaction in deforming polymers: Applications to microlithography
    • Ph.D. Thesis, University of California, Berkeley
    • Vijalapura PK. Numerical simulation of solvent diffusion and reaction in deforming polymers: Applications to microlithography. Ph.D. Thesis, University of California, Berkeley, 2004.
    • (2004)
    • Vijalapura, P.K.1
  • 40
    • 0003862145 scopus 로고
    • Modeling of positive-tone silylation processes for 193-nm lithography
    • Hartney MA. Modeling of positive-tone silylation processes for 193-nm lithography. Journal of Vacuum Science and Technology B 1993; 11:681-687.
    • (1993) Journal of Vacuum Science and Technology B , vol.11 , pp. 681-687
    • Hartney, M.A.1
  • 43
    • 26844470268 scopus 로고
    • Physical and numerical modelling in filled elastomeric systems
    • Ph.D. Thesis, Stanford University
    • Govindjee S. Physical and numerical modelling in filled elastomeric systems. Ph.D. Thesis, Stanford University, 1991.
    • (1991)
    • Govindjee, S.1
  • 44


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