메뉴 건너뛰기




Volumn 199, Issue 1-4, 2009, Pages 158-168

On the solution of the Fokker-Planck equation using a high-order reduced basis approximation

Author keywords

Fokker Planck equation; Non Newtonian fluids; Reduced basis functions; Spectral methods

Indexed keywords

BASIS FUNCTIONS; DIMENSIONAL SUBSPACE; DISCRETISATION; FENE MODEL; HIGH-DIMENSIONAL; HIGH-ORDER; NON-LINEAR; NON-NEWTONIAN FLUIDS; NUMBER OF DEGREES OF FREEDOM; NUMERICAL APPROXIMATIONS; NUMERICAL RESULTS; NUMERICAL SCHEME; NUMERICAL SOLUTION; OPTIMAL BASIS; POLYMER DYNAMICS; REDUCED BASIS FUNCTIONS; REDUCED BASIS METHODS; REDUCED BASIS TECHNIQUE; REDUCED-BASIS APPROXIMATION; SOLUTION SPACE; SPECTRAL ELEMENT; SPECTRAL METHODS;

EID: 70449363611     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2009.09.028     Document Type: Article
Times cited : (24)

References (22)
  • 1
    • 33751260933 scopus 로고    scopus 로고
    • A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids
    • Ammar A., Mokdad B., Chinesta F., and Keunings R. A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J. Non-Newtonian Fluid Mech. 139 (2006) 153-176
    • (2006) J. Non-Newtonian Fluid Mech. , vol.139 , pp. 153-176
    • Ammar, A.1    Mokdad, B.2    Chinesta, F.3    Keunings, R.4
  • 2
    • 34249706773 scopus 로고    scopus 로고
    • A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory of modeling of complex fluids. Part II: transient simulation using space-time separated representations
    • Ammar A., Mokdad B., Chinesta F., and Keunings R. A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory of modeling of complex fluids. Part II: transient simulation using space-time separated representations. J. Non-Newtonian Fluid Mech. 144 (2006) 8-121
    • (2006) J. Non-Newtonian Fluid Mech. , vol.144 , pp. 8-121
    • Ammar, A.1    Mokdad, B.2    Chinesta, F.3    Keunings, R.4
  • 3
    • 0031097299 scopus 로고    scopus 로고
    • Combined Brownian dynamics and spectral simulation of the recovery of polymeric fluids after shear flow
    • Bell T.W., Nyland G.H., de Pablo J.J., and Graham M.D. Combined Brownian dynamics and spectral simulation of the recovery of polymeric fluids after shear flow. Macromolecules 30 (1997) 1806-1812
    • (1997) Macromolecules , vol.30 , pp. 1806-1812
    • Bell, T.W.1    Nyland, G.H.2    de Pablo, J.J.3    Graham, M.D.4
  • 5
    • 0033567201 scopus 로고    scopus 로고
    • Variance reduction methods for CONNFFESSIT-like simulations
    • Bonvin J., and Picasso M. Variance reduction methods for CONNFFESSIT-like simulations. J. Non-Newtonian Fluid Mech. 84 (1999) 191-215
    • (1999) J. Non-Newtonian Fluid Mech. , vol.84 , pp. 191-215
    • Bonvin, J.1    Picasso, M.2
  • 6
    • 0042657876 scopus 로고    scopus 로고
    • Aa fast solver for Fokker-Planck equation applied to viscoelastic flows calculations: 2D FENE model
    • Chauvière C., and Lozinski A. Aa fast solver for Fokker-Planck equation applied to viscoelastic flows calculations: 2D FENE model. J. Comput. Phys. 189 (2003) 607-625
    • (2003) J. Comput. Phys. , vol.189 , pp. 607-625
    • Chauvière, C.1    Lozinski, A.2
  • 7
    • 0042023889 scopus 로고    scopus 로고
    • An efficient technique for simulations of viscoelastic flows, derived from the Brownian configuration field method
    • Chauvière C., and Lozinski A. An efficient technique for simulations of viscoelastic flows, derived from the Brownian configuration field method. SIAM J. Sci. Comput. 24 (2003) 1823-1837
    • (2003) SIAM J. Sci. Comput. , vol.24 , pp. 1823-1837
    • Chauvière, C.1    Lozinski, A.2
  • 8
  • 9
    • 0022029535 scopus 로고
    • Viscosity, first normal-stress coefficient and molecular stretching dilute polymer solutions
    • Fan X.J. Viscosity, first normal-stress coefficient and molecular stretching dilute polymer solutions. J. Non-Newtonian Fluid Mech. 17 (1985) 125-144
    • (1985) J. Non-Newtonian Fluid Mech. , vol.17 , pp. 125-144
    • Fan, X.J.1
  • 10
    • 0033567301 scopus 로고    scopus 로고
    • Simulation of fibre suspension flows by the Brownian configuration field method
    • Fan X.J., Phan-Thien N., and Zheng R. Simulation of fibre suspension flows by the Brownian configuration field method. J. Non-Newtonian Fluid Mech. 84 (1999) 257-274
    • (1999) J. Non-Newtonian Fluid Mech. , vol.84 , pp. 257-274
    • Fan, X.J.1    Phan-Thien, N.2    Zheng, R.3
  • 11
    • 0029292076 scopus 로고
    • CONNFFESSIT approach for solving a two-dimensional viscoelastic flow problem
    • Feigl K., Laso M., and Öttinger H.C. CONNFFESSIT approach for solving a two-dimensional viscoelastic flow problem. Macromolecules 28 (1995) 3261-3274
    • (1995) Macromolecules , vol.28 , pp. 3261-3274
    • Feigl, K.1    Laso, M.2    Öttinger, H.C.3
  • 12
    • 0000137599 scopus 로고    scopus 로고
    • Viscoelastic flow through fibrous media using the CONNFFESSIT approach
    • Hua C.C., and Schieber J.D. Viscoelastic flow through fibrous media using the CONNFFESSIT approach. J. Rheol. 42 (1998) 477-491
    • (1998) J. Rheol. , vol.42 , pp. 477-491
    • Hua, C.C.1    Schieber, J.D.2
  • 14
    • 0027608224 scopus 로고
    • Calculation of viscoelastic flow using molecular models: the CONNFFESSIT approach
    • Laso M., and Öttinger H.C. Calculation of viscoelastic flow using molecular models: the CONNFFESSIT approach. J. Non-Newtonian Fluid Mech. 47 (1993) 1-20
    • (1993) J. Non-Newtonian Fluid Mech. , vol.47 , pp. 1-20
    • Laso, M.1    Öttinger, H.C.2
  • 15
    • 0038680697 scopus 로고    scopus 로고
    • A Fokker-Planck simulation of fast flows of concentrated polymer solutions in complex geometries
    • Lozinski A., Chauvière C., Fang J., and Owens R.G. A Fokker-Planck simulation of fast flows of concentrated polymer solutions in complex geometries. J. Rheol. 47 (2003) 535-561
    • (2003) J. Rheol. , vol.47 , pp. 535-561
    • Lozinski, A.1    Chauvière, C.2    Fang, J.3    Owens, R.G.4
  • 16
    • 7744240417 scopus 로고    scopus 로고
    • A Fokker-Planck-based numerical method for modelling non-homogeneous flows of dilute polymeric solutions
    • Lozinski A., Owens R.G., and Fang J. A Fokker-Planck-based numerical method for modelling non-homogeneous flows of dilute polymeric solutions. J. Non-Newtonian Fluid Mech. 122 (2004) 273-286
    • (2004) J. Non-Newtonian Fluid Mech. , vol.122 , pp. 273-286
    • Lozinski, A.1    Owens, R.G.2    Fang, J.3
  • 17
    • 1342339727 scopus 로고    scopus 로고
    • Wavelet discretizations of parabolic integrodifferential equations
    • Petersdorff T.V., and Schwab C. Wavelet discretizations of parabolic integrodifferential equations. SIAM J. Numer. Anal. 41 (2003) 159-180
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 159-180
    • Petersdorff, T.V.1    Schwab, C.2
  • 18
    • 1342326246 scopus 로고    scopus 로고
    • Numerical solution of parabolic equations in high dimensions
    • Petersdorff T.V., and Schwab C. Numerical solution of parabolic equations in high dimensions. ESAIM: M2AN 38 (2004) 93-127
    • (2004) ESAIM: M2AN , vol.38 , pp. 93-127
    • Petersdorff, T.V.1    Schwab, C.2
  • 19
    • 33748201070 scopus 로고    scopus 로고
    • Spectral element approach to the simulation of viscoelastic flows using Brownian configuration fields
    • Phillips T.N., and Smith K.D. Spectral element approach to the simulation of viscoelastic flows using Brownian configuration fields. J. Non-Newtonian Fluid Mech. 138 (2006) 98-110
    • (2006) J. Non-Newtonian Fluid Mech. , vol.138 , pp. 98-110
    • Phillips, T.N.1    Smith, K.D.2
  • 20
    • 0033133959 scopus 로고    scopus 로고
    • On the hysteretic behaviour of dilute polymer solutions in relaxation following extensional flow
    • Sizaire R., Lielens G., Jaumain I., Keunings R., and Legat V. On the hysteretic behaviour of dilute polymer solutions in relaxation following extensional flow. J. Non-Newtonian Fluid Mech. 82 (1999) 233-253
    • (1999) J. Non-Newtonian Fluid Mech. , vol.82 , pp. 233-253
    • Sizaire, R.1    Lielens, G.2    Jaumain, I.3    Keunings, R.4    Legat, V.5
  • 21
    • 0003424374 scopus 로고    scopus 로고
    • Society for Industrial and Applied Mathematics, Philadelphia
    • L.N. Trefethen, D. Bau, Numerical Linear Algebra, Society for Industrial and Applied Mathematics, Philadelphia, 1997.
    • (1997) Numerical Linear Algebra
    • Trefethen, L.N.1    Bau, D.2
  • 22
    • 12444298998 scopus 로고    scopus 로고
    • A QMC approach for high dimensional Fokker-Planck equations modelling polymeric liquids
    • Venkiteswaran G., and Junk M. A QMC approach for high dimensional Fokker-Planck equations modelling polymeric liquids. Math. Comput. in Simulat. 68 (2005) 43-56
    • (2005) Math. Comput. in Simulat. , vol.68 , pp. 43-56
    • Venkiteswaran, G.1    Junk, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.